Chapter 11, Problem 19CT

To determine

To calculate:the probability that random selected students have part time jobs.

Answer to Problem 19CT

the probability forrandom selected students have part time jobs is $\frac{973}{7980}$ .

Explanation of Solution

Given information :

total students = $400$

part time job students = $35\%$

Formula used:

  $P{}_r=\frac{n!}{\left(n-r\right)!}$

Calculation : to find the probability, first find the total number of students who has part time job,

  $\begin{array}{l}35\%of400\\ .35·400\text{ [convert pencent into decimal]}\\ 140\text{ [multiply]}\end{array}$

Number of possibilities to choose two students from total students,

  $\begin{array}{l}P{}_r=\frac{n!}{\left(n-r\right)!}\\ P{}_2=\frac{400!}{\left(400-2\right)!}\text{ [substitute n by 400 and r by 2]}\\ P{}_2=\frac{400!}{398!}\text{ [subtract]}\\ P{}_2=159600\text{ [expand factors, divide out common factors and multiply]}\end{array}$

now choose two students from part time job students,

  $\begin{array}{l}P{}_2=\frac{140!}{\left(140-2\right)!}\text{ [substitute n by 140 and r by 2]}\\ P{}_2=\frac{140!}{\left(138\right)!}\text{ [subtract]}\\ P{}_2=19460\text{ [expand factorial and divide out common factors and multiply]}\end{array}$

Probability = $\frac{19460}{159600}$

= $\frac{973}{7980}$

Hence,the probability for random selected students have part time jobs is $\frac{973}{7980}$ .