Answer:
A. $130.50
B. 150%
C. 50%
Step-by-step explanation:
First, find 50% of 87 and add it to find the new price.
87 x 0.5 = 43.5
87 + 43.5 = 130.5
Then, find the percent by doing 130.5 ÷ 87, which is 150%
Calculate the percent increase by doing (130.5-87) ÷ 87, which is 50%
Answer:
see below
Step-by-step explanation:
First find the markup
87* 50%
87*.50
43.50
Add this to the wholesale price
87+43.50 =130.50
This is what they charge the customer
This is 150% percent of the wholesale price
100% + 50% = 150%
To find the percent increase
Take the new price and subtract the wholesale price
Then divide by the wholesale price
(130.50-87)/87 =50 % increase
Express 1400 as a product of its prime factors in index form
Answer:
[tex]2^3 X5^2 X7[/tex]
Step-by-step explanation:
Given the number: 1400
A number is said to be prime when it can only be divided by 1 and itself.
We can express 1400 as a product of its prime numbers by gradually decomposing it into smaller units.
[tex]1400=14X100\\14=2X7\\100=10X10=2X5X2X5\\$Therefore:\\1400=2 X 7 X 2 X 5 X 5 X 5\\Reorganising\\1400=2 X 2 X 2 X 5 X 5 X 7\\Therefore, 1400 expressed as a product of its prime factors is:\\1400=2^3 X5^2 X7[/tex]
NEED HELP FAST!The weather report says the temperature is 20°C and will drop 5°C per hour for the next 6 hours. Daryl plans to be gone for at least 6 hours, and he has a plant outside. If he wants the plant to remain in temperatures above –10°C, should Daryl move his plant to a warmer location before leaving?
An inequality to model the problem is .
The solution is .
Answer:
no he should be fine it will be -10C when he gets back
Step-by-step explanation:
Answer:
The weather report says the temperature is 20°C and will drop 5°C per hour for the next 6 hours. Daryl plans to be gone for at least 6 hours, and he has a plant outside. If he wants the plant to remain in temperatures above –10°C, should Daryl move his plant to a warmer location before leaving?
An inequality to model the problem is
✔ 20 - 5x > -10
.
The solution is
✔ x < 6
.
Step-by-step explanation: no one could answer this write so here.
College Students and Drinking Habits: A public health official is studying differences in drinking habits among students at two different universities. They collect a random sample of students independently from each of the two universities and ask each student how many alcoholic drinks they consumed in the previous week. Sample Statistics:
size(n) Mean (X) SD(s)
sample1 40 6.9 2.3
sample 2 49 5.7 1.9
The official conducts a two -sample t-test to determine whether these data provide significant evidence that students at University 1 drink more than students at University 2. The test statistics is t=2.64 with a P-value 0.005. Which of the following is an appropriate conclusion?
A) The samples provide significant evidence that students at University 1 drink more than students at university 2.
B) The samples do not provide statistically significant evidence.
C) We ca not use the t-test in this case because the variables (number of drinks) are likely skewed to the right at each university.
Answer:
Option A
Step-by-step explanation:
From the outlined data, the p value calculated was given as 0.005 which is way less than 0.05, thus we will reject the null hypothesis that there is no difference in drinking habit among students at two different universities. We can then conclude that the samples provide significant evidence that students at University 1 drink more than students at university 2.
An airplane climbs at an angle of 2.7" from an altitude of 4500 ft to an altitude of 5600 ft. How far does the airplane travel as it climbs as
measured along the horizontal?
Answer:
23,325 ft, about 4.42 miles
Step-by-step explanation:
The geometry of the situation can be modeled by a right triangle, where the side adjacent to the 2.7° angle of climb is the horizontal distance, and the side opposite is the vertical change in altitude. That change is ...
5600 ft -4500 ft = 1100 ft
and the angle relation is ...
tan(2.7°) = opposite/adjacent = (1100 ft)/(horizontal distance)
Multiplying this equation by (horizontal distance)/tan(2.7°) gives ...
horizontal distance = (1100 ft)/tan(2.7°) ≈ 23,325 ft
Dividing this by 5280 ft/mi gives ...
horizontal distance ≈ 4.42 mi
The airplane travels about 23,325 ft, or 4.42 miles, horizontally as it climbs.
You took 6 math quizzes. Your scores are: 89, 96, 92, 84, 94, 100. Mrs. Edwards gave you the choice to pick the mean, median, mode or range to be your report card grade. Which one would you pick and why?
Answer:
Median. It has the highest grade.
Step-by-step explanation:
Mean: 92.5
Median: 93
Mode: no mode (all numbers occur only once)
Range: range is 11 (this would be a terrible grade)
Because the median has the highest grade, you would want to pick it.
If you want/ need me to show work or explain just let me know
Also, if my answer helps please consider giving me brainliest.
A marketing study conducts 60 significance tests about means and proportions for several groups. Of them, 3 tests are statistically significant at the 0.05 level. The study's final report stresses only the tests with significant results, not mentioning the other 57 tests. What is misleading about this?
Answer:
hello your question lacks the required options attached is a picture of the complete question
One would expect about 5% of tests to be significant just by chance if the null hypothesis is true, and for 60 tests, this is 0.05(60) = 3 tests. This could explain why these tests are statistically significant.
Step-by-step explanation:
What is misleading about this is the study's final report because this marketing study was carried out with a level of significance of 5% (0.05) which means that if we carry the same study with varying sample data we will mostly like arrive at a conclusion against our null conclusion 5% of the time and this is not good for the the study because it is a type 1 error and has to be eliminated and it cannot be eliminated totally .
hence One would expect about 5% of tests to be significant just by chance if the null hypothesis is true, and for 60 tests, this is 0.05(60) = 3 tests. This could explain why these tests are statistically significant.
We are told that the marketing study conducts 60 tests and that 3 tests are statistically significant at the 0.05 level, in addition to this the study's final report emphasizes only the tests with significant results without mentioning the other 57 tests.
We can interpret it as follows:
By the 0.05 level, we mean that 5% of the tests are significant by chance when the null hypothesis is true.
Here 5% of the 60.
60 * 0.05 = 3
Therefore it only mentions 3 tests and does not mention the other 57 tests, which in itself is misleading because all 60 tests should be fully mentioned in the final report.
Determine where f(x) is discontinuous. Justify your answer.
f(x)=x^2+x-2/x-1
Answer:x=1
Step-by-step explanation:
Given
[tex]F(x)=\dfrac{x^2+x-2}{x-1}[/tex]
F(x) will be discontinuous at x=1 because value of f(x) is undefined at that point.
F(x) is defined for all values of x except at x=1
Of 1,050 randomly selected adults, 360 identified themselves as manual laborers, 280 identified themselves as non-manual wage earners, 250 identified themselves as mid-level managers, and 160 identified themselves as executives. In the survey, 82% of manual laborers preferred trucks, 62% of non-manual wage earners preferred trucks, 54% of mid-level managers preferred trucks, and 26% of executives preferred trucks.
Construct a 95% confience interval for the percentage of executives that preferred trucks. ( I know for sure that the answer is +or- 6.82%, but I need to know how to get this.)
Answer:
We can claim with 95% confidence that the proportion of executives that prefer trucks is between 19.2% and 32.8%.
Step-by-step explanation:
We have a sample of executives, of size n=160, and the proportion that prefer trucks is 26%.
We have to calculate a 95% confidence interval for the proportion.
The sample proportion is p=0.26.
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.26*0.74}{160}}\\\\\\ \sigma_p=\sqrt{0.0012}=0.0347[/tex]
The critical z-value for a 95% confidence interval is z=1.96.
The margin of error (MOE) can be calculated as:
[tex]MOE=z\cdot \sigma_p=1.96 \cdot 0.0347=0.068[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=p-z \cdot \sigma_p = 0.26-0.068=0.192\\\\UL=p+z \cdot \sigma_p = 0.26+0.068=0.328[/tex]
The 95% confidence interval for the population proportion is (0.192, 0.328).
We can claim with 95% confidence that the proportion of executives that prefer trucks is between 19.2% and 32.8%.
A regular hexagonal prism has sides of 4 cm for the hexagonal bases and is 10 cm in height. Find its exact
volume. Then, quickly find the exact volume of a regular hexagonal pyramid inscribed in the prism. If you
don’t have a 3 in your answers, something’s gone wrong.
Answer:
Exact volume of the hexagonal prism = 240√3 cm³
Exact volume of the hexagonal pyramid = 80√3 cm³
Step by step explanation:
Volume of hexagonal prism = [(3√3)/2]×a²h
Where a = base edge
h = height
From the question,
a = 4cm, h = 10cm
V = [(3√3)/2]×(4)²×(10)
V = (3√3) × 160/2
V = 240√3 cm³
Exact volume of the hexagonal prism = 240√3 cm³
Volume of hexagonal pyramid = [(√3)/2]×a²h
a = 4cm, h = 10cm
V = [(√3)/2]×(4)²×(10)
V = (√3) × 160/2
V = 80√3 cm³
Exact volume of the hexagonal pyramid = 80√3 cm³
You can afford a $850 per month mortgage payment. You've found a 30 year loan at 8% interest.
a) How big of a loan can you afford?
$
Incorrect
b) How much total money will you pay the loan company?
$
Incorrect
c) How much of that money is interest?
$
Incorrect
Answer:
a) $115,840.97
b) $306,000
c) $190,159.03
Step-by-step explanation:
Loan payment calculations can be done using the amortization formula:
A = P(r/12)/(1 -(1 +r/12)^(-12t))
where A is the monthly payment, P is the principal value of the loan, r is the annual interest rate, and t is the loan duration in years.
a) Loan amountThe principal amount of the loan can be found by filling in the given values and solving for P.
850 = P(0.08/12)/(1 -(1 +0.08/12)^(-12·30))
P = 850(1 -1.0066667^-360)/0.0066667 ≈ 850×136.283494
P = 115,840.97
You could afford a loan of $115,840.97.
b) Total paidThe total amount paid is the sum of 360 payments of $850 each:
360 × $850 = $306,000
You will pay $306,000 to the loan company.
c) InterestThe amount of interest is the difference between the amount paid and the amount borrowed:
$306,000 -115,840.97 = $190,159.03
$190,159.03 of the amount paid is interest.
__
Additional comment
A variety of apps, calculators, and spreadsheets can do these calculations for you. The result from one of these calculators is attached. The PV is the Present Value of the series of 360 payments of $850 each. It is the loan amount.
Suppose that the exam scores for students in a large university course are normally distributed with an unknown mean and standard deviation. The scores of 42 randomly sampled students in the course are used to estimate the mean of the population. What t-score should be used to find the 99% confidence interval for the population mean? df...4041424344t0.10…1.3031.3031.3021.3021.301t0.05…1.6841.6831.6821.6811.680t0.025…2.0212.0202.0182.0172.015t0.01…2.4232.4212.4182.4162.414t0.005…2.7042.7012.6982.6952.692 Use the portion of the table above or a calculator. If you use a calculator, round your answer to three decimal places.
Answer:
Critical value t-score=2.701.
Step-by-step explanation:
When we calculate a confidence interval with an unknown population standard deviation, we estimate it from the sample standard deviation and use the t-score instead of the z-score.
The critical value for t depends on the level of confidence and the degrees of freedom.
If the sample size is 42, the degrees of freedom are:
[tex]df=n-1=42-1=41[/tex]
For a confidence level of 99% and 41 degrees of freedom, the critical value of t is t=2.701.
What’s the correct answer for this?
Answer:
the third option
Step-by-step explanation:
the union of two sets of numbers just has to show all the numbers that are in the two sets, meaning if both sets have the same number, it is only shown once in the union
Simplify the following expression. −3√84x3
Answer:
-18root7
Step-by-step explanation:
-3root 84*3
-3root4*7*3*3
-3(2*3)root7
-18root7
Kendra found this relationship between the quantities in the table.
1
3
4
2.
150
5
375
y
75
225
300
Multiply x by 7.5 to get y
Which error did Kendra make?
Kendra should have added 75 to the x-values to get the y-values
Kendra should have added 7.5 to the x-values to get the y-values
Kendra should have multiplied the x-values by 75 to get the y-values
Kendra should have multiplied the x-values by 25 to get the y-values
HELP IM TIMED
Answer:
Kendra should have multiplied the x-values by 75 to get the y-values
Step-by-step explanation:
Given
Table
X|| Y
1 || 75
2 || 150
3 || 225
4 || 300
5 || 375
Given that Kendra multiply x by 7.5 to get y
The relationship of x and y can be calculated as thus;
y = rx
Where y and x are the values at the y and x column respectively and r is the constant of proportionality
When y = 75, x = 1.
Plug in these values in the above formula
y = rx becomes
75 = r * 1
75 = r
r = 75
When y = 150, x = 2
150 = r * 2
Multiply both sides by ½
150 * ½ = r * 2 * ½
75 = r
r = 75
When y = 225, x = 3
225 = r * 3
Multiply both sides by ⅓
225 * ⅓ = r * 3 * ⅓
75 = r
r = 75
Notice that r remains 75 and the difference between y values is 75
If you apply these formula on when y = 300 or 375 and when x = 4 or 5, the constant of proportionality will remain The value of 75.
Hence, Kendra mistake is that; Kendra should have multiplied the x-values by 75 to get the y-values
Please answer this correctly
Answer:
[tex]10.71 yd[/tex]
Step-by-step explanation:
First let's find the radius of the quarter circle.
[tex]area =\frac{1}{4} \pi {r}^{2} \\ 7.065 = \frac{1}{4} *3.14 {r}^{2} \\ \frac{7.065}{3.14} = \frac{1}{4} * \frac{3.14 {r}^{2} }{3.14} \\ 9 = {r}^{2} \\ \sqrt{9} = r \\ 3 yd= r[/tex]
Now let's find the arc length of this quarter circle.
[tex] \frac{90}{360} \times 2\pi \: r \\ \frac{1}{4} \times 2 \times 3.14 \times 3 \\ = \frac{9.42}{4} \\ = 4.71yd \\ [/tex]
Now let's find the perimeter[tex]perimeter \\ = arc \: \: length + radius + radius \\ = 4.71 + 3 + 3 \\ = 10.71yd[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Answer:
10.71 ydStep-by-step explanation:
The formula of an area of a circle:
[tex]A=\pi r^2[/tex]
r - radius
The formula of an area of a quarter circle:
[tex]A=\dfrac{1}{4}\pi r^2[/tex]
We have the area of a quarter circle:
[tex]A=7.065\ yd^2[/tex]
Substitute to the formula and solve for r :
[tex]\dfrac{1}{4}\pi r^2=7.065[/tex] multiply both sides by 4
[tex]4\cdot\dfrac{1}{4}\pi r^2=7.065\cdot4\\\\\pi r^2=28.26[/tex]
Use 3.14 for π
[tex]3.14r^2=28.26[/tex] divide both sides by 3.14
[tex]\dfrac{3.14r^2}{3.14}=\dfrac{28.26}{3.14}\\\\r^2=9\to r=\sqrt9\\\\\boxed{r=3\ yd}[/tex]
The circumference of this figure consists of an arc (quarter of a cirumference of a circle) and two radiuses.
The formula of a circumference of a circle:
[tex]C=2\pi r[/tex]
The formula of a quarter of a cicrumference of a circle:
[tex]L=\dfrac{1}{4}\cdot2\pi r[/tex]
Substitute
[tex]L=\dfrac{1}{4}\cdot2\pi\cdot3=1.5\pi[/tex]
Use 3.14 for π
[tex]L=1.5(3.14)=4.71\ yd[/tex]
The perimeter of a quarter circle:
[tex]P=4.71+2(3)=4.71+6=10.71\ yd[/tex]
Rebecca made an equation that models the height of a tree since she moved in. The height of the tree, h=3t+40 where H=height (in feet) and t=years. How big was the height of the tree when she moved in?
Answer:
40 feet
Step-by-step explanation:
The number of years since she moved in when she just moved in is 0,
thus, t=0
So,
H=3*0+40
H=40 feet
The height of the tree when Rebecca just moved in was 40 feet
Why do we think 0! = 1?
[tex]4!=4\times3\times2\times1=24\\3!=3\times2\times1=6\\2!=2\times1\\1!=1\\0!=?[/tex]
Notice that when we go from 4! to 3! , we divide by 4.
(Because [tex]4!\div 4 = 4\times3\times2\times1\div4=3\times2\times1=3![/tex] the 4's cancel)
And when we go from 3! to 2! , we divide by 3, and etc.
We can use this pattern to see why 0! = 1.
[tex]4!=4\times3\times2\times1=24\\3! = 4!\div4=24\div4=6\\2!=3!\div3=6\div3=2\\1!=2!\div2=2\div2=1\\0!=1!\div1=1\div1=1[/tex]
And so by following the pattern, we determine that 0! = 1
-------------------------------
Note:
There are no factorials of negative numbers, and we can use the pattern to show why:
[tex]0!=1\\-1!=0!\div0=1\div0=???!!??!?[/tex]
You can't divide a number by 0, therefore -1! doesn't exist, so -2! doesn't exist and so on. So you can't do the factorial of any negative number.
(Or at least there no real solutions to negative factorials)
------------------------
1. What shape of the distribution is best modeled by a normal curve? *
Answer:
A symmetric bell shape
Step-by-step explanation:
A normal curve has a symmetrical bell shaped curve, this can be seen when a histogram is constructed with values that are normally distributed, the resulting shape is symmetrical and has a bell shape.
A street is 149m long is covered in snow. City workers are using a snowplow to clear the street. The snowplow has tires that are 1.7m in diameter. How many times does a tire have to turn in traveling the length of the street
Answer:
Approximately 28 times
Step-by-step explanation:
The tires are circular in shape.
We first need to find the circumference of the tire and then divide the length of the road by that circumference.
The circumference of a circle is given as:
C = πD
where D = diameter
The diameter of the tires is 1.7 m. Its circumference is therefore:
C = π * 1.7 = 5.34 m
Therefore, the number of times that the tire has to turn in traveling the length of the street is:
149 / 5.34 = 27.9 ≅ 28
Please answer this correctly
Answer:
17.7
Step-by-step explanation:
62.3-7=55.3
55.3-19.9=35.4
35.4/2 = 17.7
brainliest pzz
Answer:
The value of s is 17.7mm.
Step-by-step explanation:
Given that perimeter of a shape happens when all sides are add up together. So for this question :
[tex]perimeter = 7 + 19.9 + s + s[/tex]
[tex]perimeter = 26.9 + 2s[/tex]
Let perimeter = 62.3mm,
[tex]62.3 = 26.9 + 2s[/tex]
[tex]2s = 62.3 - 26.9[/tex]
[tex]2s = 35.4[/tex]
[tex]s = 35.4 \div 2[/tex]
[tex]s = 17.7mm[/tex]
A method currently used by doctors to screen patients for a certain type of cancer fails to detect cancer in 15% of the patients who actually have the disease. A new method has been developed that researchers hope will be able to detect cancer more accurately. A random sample of 80 patients known to this type of cancer is screened using the new method and the method failed to detect the cancer in 8 patients. At the 5% level of significance, can the researchers conclude that the new method is better than the one currently in use? (Can they conclude that the new method fails to detect cancer in less than 15% of the patients who actually have the disease?)
Answer:
A technique presently used through docs to display screen ladies for breast most cancers fails to observe most cancers in 15% of the girls who without a doubt have the disease. A random pattern of eighty girls acknowledged to have breast most cancers are to be screened the use of a new technique that researchers suppose will be capable to realize most cancers greater accurately. At the 0.05 stage of significance, the researchers will be capable to conclude that the new approach is higher than the present day one if the fantastic.
Answer::: greater than 1.645
What’s the correct answer for this?
Answer:
Arc CR = 90 deg
=> angle CBR = 90 deg
=> angle CBV = 90 deg
=> 3x + 4 = 90
=> 3x = 86
=> x =~28.7 deg
=> Option A is correct
Hope this helps!
:)
Answer:
A: x = 28.7
Step-by-step explanation:
Since VR is the diameter and CB is bisecting it so arcVC= arcCR and
<CBV = <CBR
NOW
3x+4 = 90
3x = 90-4
3x = 86
Dividing both sides by 3
x ≈ 28.7
I am completely stumped...
Answer:
x=25[tex]\sqrt{2}[/tex]
Step-by-step explanation:
the hypotenuse is equal to a leg times the square root of 2. which means to find the leg with the hyp given. you take [tex]\frac{50}{\sqrt{2} }[/tex] which then translates to 50 root 2/2=x therefore 25[tex]\sqrt{2}[/tex]
What is the value (hundredth) of the ratio of the circumference of a circle
to its diameter?
Answer:
3.14Step-by-step explanation:
the circumference of a circle = Diameter × π
in other words ,the ratio of the circumference of a circle to its diameter is π
and we know that π = 3.14159265358979...
if we round it to the hundredth we get 3.14
What three numbers add up to 57, with the first number being 12
The answer is 12, 15, 30
Tickets for a concert were \$5$5dollar sign, 5 for each child and \$8$8dollar sign, 8 for each adult. At one of the concerts, each adult brought 444 children with them, and 101010 children attended without an adult. The total ticket sales were \$1{,}730$1,730dollar sign, 1, comma, 730. Which of the following systems of equations can be solved to determine the number of children, ccc, and adults, aaa, who attended the concert?
Answer:
Step-by-step explanation:
Let c represent the number of children that attended the concert.
Let a represent the number of adults that attended the concert.
At one of the concerts, each adult brought 4 children with them, and 10 children attended without an adult. This means that the number of children that attended is
c = 4a + 10
Tickets for a concert were $5 for each child and $8 for each adult. The total ticket sales were $1730. It means that
5c + 8a = 1730
Therefore, the systems of equations that can be solved to determine the number of children, c, and adults that attended the concert is
c = 4a + 10
5c + 8a = 1730
Answer:
c = 4a + 10
5c + 8a = 1730
Step-by-step explanation:
In a sociology course, the professor informed the students of a recent exam ratio of 9:7:2 for As, Bs , and Cs. If 72 students scoring C or better completed the exam l, how many students received Bs?
Answer:
28
Step-by-step explanation:
To solve this, I would first add up the total of the numbers in the ratio.
9 + 7 + 2 = 18
Then, I would divide 72 by that number.
72/18 = 4.
Finally, I would multiply that quotient by 7 because 7 is the number in the ratio for B's.
4 x 7 = 28
what’s the correct answer for this?
Answer:
see below
Step-by-step explanation:
The probability a member is a girl is independent of the probability that a member plays sports if the fraction of members that are girls does not depend on whether the member plays sports or not.
That is, the fraction of members that are girls will be the same for sports players and non-sports players.
_____
Examples
(a) Suppose we have a membership that consists of ...
1 girl and 1 boy who play sports (as many girls as boys), and 1 girl who does not play sports.
We want to see if p(g) and p(s) are independent, so we compute p(g) and p(g|s).
p(g) = 2/(2+1) = 2/3
p(g|s) = p(g&s)/p(s) = (1/3)/(2/3) = 1/2 . . . . not independent
__
(b) Suppose we have a membership that consists of ...
1 girl and 1 boy who play sports, and 2 girls and 2 boys who don't play sports (girls are half the members who play, and half the members who don't play).
p(g) = 3/6 = 1/2
p(g|s) = p(g&s)/p(s) = (2/6)/(4/6) = 2/4 = 1/2 . . . . independent
__
(c) Suppose we have a membership that consists of ...
2 girls and 1 boy who play sports, and 2 boys and 1 girl who do not play sports (fraction of girl players = fraction of boy non-players)
p(g) = 3/6 = 1/2
p(g|s) = p(g&s)/p(s) = (2/6)/(3/6) = 2/3 . . . . not independent
__
(d) Suppose we have a membership that consists of ...
1 girl and 1 boy who play sports, and 1 girl who does not play sports (as many girls play as do not)
p(g) = 2/3
p(g|s) = p(g&s)/p(s) = (1/6)/(2/6) = 1/2 . . . . not independent
__
These examples match our selection of the 2nd choice as being the one that demonstrates independence.
Write a compound inequality to represent all of the numbers between -4 and 6.
Answer:
-4<X<6
Step-by-step explanation:
Let the number be X
Hence -4<X<6
A certain company sends 35% of its overnight mail parcels via express delivery service 1 and the rest by express delivery service 2. Express delivery service 1 has a record of 3.0% of packages being delivered late and express delivery service 2 has a record of 2.0% of packages being delivered late. A package was delivered late. What is the probability that a late package was delivered by express delivery service 2
Answer:
55.32% probability that a late package was delivered by express delivery service 2
Step-by-step explanation:
Bayes Theorem:
Two events, A and B.
[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]
In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.
In this question:
Event A: Late delivery.
Event B: Service 2 was used.
A certain company sends 35% of its overnight mail parcels via express delivery service 1 and the rest by express delivery service 2.
100 - 35 = 65%.
So [tex]P(B) = 0.65[/tex]
Service 2 has a record of 2.0% of packages being delivered late.
This means that [tex]P(A|B) = 0.02[/tex]
Probability of a late delivery.
35% from service 1. Of those, 3% are late.
65% from service 2. Of those, 2% are late.
So
[tex]P(A) = 0.35*0.03 + 0.65*0.02 = 0.0235[/tex]
What is the probability that a late package was delivered by express delivery service 2
[tex]P(B|A) = \frac{0.65*0.02}{0.0235} = 0.5532[/tex]
55.32% probability that a late package was delivered by express delivery service 2