Chapter 13, Problem 26SGR

(a)

To determine

If a bag contains 40 raffle tickets from 1 to 40 then find the probability that a chosen number is an even number or less than 5.

Answer to Problem 26SGR

The probability of drawing an even or less than 5 is $\frac{11}{20}$ .

Explanation of Solution

Given information: It is given that a bag contains 40 raffle tickets from 1 to 40.

Calculation: The probability of a number to be even or less than 5 is evaluated as,

  $\begin{array}{c}P\left(\text{Even }\cup \text{ Less than 5}\right)=P\left(\text{Even}\right)+P\left(\text{Less than 5}\right)-\left(\text{Even }\cap \text{ Less than 5}\right)\\ =\frac{20}{40}+\frac{4}{40}-\frac{2}{40}\\ =\frac{22}{40}\\ =\frac{11}{20}\end{array}$

Hence the probability of drawing an even or less than 5 is $\frac{11}{20}$ .

(b)

To determine

If a bag contains 40 raffle tickets from 1 to 40 then find the probability that a chosen ticket is greater than 30 or less than 10.

Answer to Problem 26SGR

The probability of drawing a ticket greater than 30 or less than 10 is $\frac{19}{40}$ .

Explanation of Solution

Given information: It is given that a bag contains 40 raffle tickets from 1 to 40.

Calculation: The probability of a ticket to be greater than 30 or less than 10 is evaluated as,

  $\begin{array}{c}P\left(>30\cup <10\right)=P\left(>30\right)+P\left(<10\right)-\left(>30\cap <10\right)\\ =\frac{10}{40}+\frac{9}{40}-\frac{0}{40}\\ =\frac{19}{40}\end{array}$

Hence the probability of drawing a ticket greater than 30 or less than 10 is $\frac{19}{40}$ .