Chapter 13.3, Problem 2CFU

To determine

To find two examples of the use of probability in newspapers or magazines and describe how probability concepts are applied.

Explanation of Solution

The First Example:

To find P (at least $3$ women) if committee of $5$ members is to be selected at random from $6$ women and $7$ men.

P (at least $3$ women) $=$ P ( $3$ women) $+$ P ( $4$ women) $+$ P ( $5$ women)

  $\begin{array}{l}=\frac{C(6,3)\cdot C(7,2)}{C(13,5)}+\frac{C(6,4)\cdot C(7,1)}{C(13,5)}+\frac{C(6,5)\cdot C(7,0)}{C(13,5)}\\ =\frac{420}{1287}+\frac{105}{1287}+\frac{6}{1287}\\ =\frac{531}{1287}\end{array}$

The Second Example:

Let A be the event of taking out $2$ bottles of fruit juice.

Let B be the event of taking out $4$ bottles of sports drink.

Total sample space $=6$

Therefore probability of event A is $P(A)=\frac{4}{6}=\frac{2}{3}$

Therefore probability of event B is $P(B)=\frac{3}{5}$

Hence,

  $\begin{array}{l}P(A\text{ and }B)=P(A)\times P(B)\\ P(A\text{ and }B)=\frac{2}{3}\times \frac{3}{5}=\frac{2}{5}\end{array}$