Chapter 12.5, Problem 32PPS

To determine

To find the probability that Jose will win on his first turn.

Answer to Problem 32PPS

The probability that Jose will win on his first turn is $\frac{11}{25}\text{ or 44\%}$ .

Explanation of Solution

Given information:

The given statement is:

“Kirsten and Jose are playing a game. Kirsten places tiles numbered $1\text{ to }50$ in a bag. Jose selects a tiles at random. If he selects a prime number or a number greater than $40$ , then he wins the game. What is the probability that Jose will win on his first turn?”

Calculation :

The probability can be calculated by:

  $\begin{array}{l}\text{P}\left(\text{prime number}\right)=\frac{15}{50}\\ \text{P}\left(\text{greater than 40}\right)=\frac{10}{50}\\ \text{P}\left(\text{prime number and greater than 40}\right)=\frac{3}{50}\\ \text{P}\left(\text{prime number or greater than 40}\right)=\frac{15}{50}+\frac{10}{50}-\frac{3}{50}\\ \text{P}\left(\text{prime number or greater than 40}\right)=\frac{22}{50}\\ \text{P}\left(\text{prime number or greater than 40}\right)=\frac{11}{25}\text{ or 44\%}\end{array}$

Hence, the probability that Jose will win on his first turn is $\frac{11}{25}\text{ or 44\%}$ .