Question

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

Answer 1

Complete Question

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Answer:

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

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

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

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

       $P(k) =  \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}$

=>       $P( u | k) = \frac{19}{111-1}$

=>       $P( u | k) = \frac{19}{110}$

So

       $ P(k \ n \  u ) =   \frac{ 19}{111} * \frac{19}{110}$

=>    $ P(k \ n \  u ) =   0.02957$