Chapter 12.3, Problem 3CYP

To determine

Tofind:the probability that a student plays varsity given that he or she is a freshman.

Answer to Problem 3CYP

It is $2.5\mathrm{\%}$ option G is correct.

Explanation of Solution

Given:

There is total of $1180$ students.

He or she is a freshman.

Concept used:

Probability formula:

  $\begin{array}{l}\mathrm{P}\left(\mathrm{A}\right)=\frac{\text{number of favourable events}}{\text{number of total events}}.\\ \mathrm{P}\left(\mathrm{A}\right)=\frac{\mathrm{n}\left(\mathrm{A}\right)}{\mathrm{n}},\mathrm{P}\left(\mathrm{B}\right)=\frac{\mathrm{n}\left(\mathrm{B}\right)}{\mathrm{n}}.\end{array}$

For a conditional probability the formula will be:

  $\mathrm{P}\left(\mathrm{A}|\mathrm{B}\right)=\frac{\mathrm{P}\left(\mathrm{A}\cap \mathrm{B}\right)}{\mathrm{P}\left(\mathrm{B}\right)}$ .

Calculation:

Here need to find the probability that a student plays varsity given that he or she is freshman.’

There is total of $1180$ students.

  $\begin{array}{l}\mathrm{P}\left(\frac{\mathrm{V}}{\mathrm{F}}\right)=\frac{\mathrm{P}\left(\mathrm{V}\text{ and }\mathrm{F}\right)}{\mathrm{P}\left(\mathrm{F}\right)}.\\ \Rightarrow \frac{7}{1180}÷\frac{276}{1180}.\\ \Rightarrow 0.02536=2.5\mathrm{\%}.\end{array}$

Hence, it is $2.5\mathrm{\%}$ option G is correct.