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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

User Ndrdm
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Complete Question

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Answer:

The value is
P(k \ n \  u ) =   0.02957

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


P(k \ n \ u ) = P(k) * P(u\ | \ k)

Here
P(k) is the probability that a senior nutrition major is selected , this is mathematically represented as


P(k) = &nbsp;(k)/(n)[\tex]</p><p>=> &nbsp; &nbsp; [tex]P(k) = &nbsp;( 19)/(111)[\tex] </p><p> and &nbsp;P( u | k) is the probability that a &nbsp;junior Nutrition &nbsp;major is selected &nbsp;given that a senior nutrition major has already been selected and this is mathematically represented as </p><p> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;[tex]P( u | k) = (u)/(n-1)

=>
P( u | k) = (19)/(111-1)

=>
P( u | k) = (19)/(110)

So


P(k \ n \ &nbsp;u ) = &nbsp; ( 19)/(111) * (19)/(110)

=>
P(k \ n \ &nbsp;u ) = &nbsp; 0.02957

There are 111 students in a nutrition class. The instructor must choose two students-example-1
User AntonyMN
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