There are 111 students in a nutrition class. The instructor must choose two students at random. What is the probability that a senior Nutrition major and then a junior Nutrition major are chosen at random
Answers
Complete Question
The complete question is shown on the first uploaded image
Answer:
The value is [tex] P(k \ n \ u ) = 0.02957[/tex]
Step-by-step explanation:
From the question we are told that
The total number of students is n = 111
The total number of senior nutrition major k = 19
The total number of junior nutrition major is u = 19
Generally the probability that a senior Nutrition major and then a junior Nutrition major are chosen at random is mathematically represented as
[tex]P(k \ n \ u ) = P(k) * P(u\ | \ k)[/tex]
Here [tex]P(k)[/tex] is the probability that a senior nutrition major is selected , this is mathematically represented as
[tex]P(k) = \frac{k}{n}[\tex]
=> [tex]P(k) = \frac{ 19}{111}[\tex]
and P( u | k) is the probability that a junior Nutrition major is selected given that a senior nutrition major has already been selected and this is mathematically represented as
[tex]P( u | k) = \frac{u}{n-1}[/tex]
=> [tex]P( u | k) = \frac{19}{111-1}[/tex]
=> [tex]P( u | k) = \frac{19}{110}[/tex]
So
[tex] P(k \ n \ u ) = \frac{ 19}{111} * \frac{19}{110} [/tex]
=> [tex] P(k \ n \ u ) = 0.02957[/tex]
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