Chapter 13, Problem 25RE

Each of the numbers 1, 2,..., 100 is written on an index card, and the cards are shuffled. If a card is selected at random, what is the probability that the number on the card is divisible by 5? What is the probability that the card selected either is a 1 or names a prime number?

To determine

To find:

a. what is the probability that the number on the card is divisible by 5?

Answer to Problem 25RE

a. $\frac{1}{5}$

Explanation of Solution

Given:

Each of the numbers 1, 2, .... 100 is written on an index card, and the cards are shuffled. A card is selected at random.

Formula used:

$P\left(E\right) = \frac{n\left(E\right)}{n\left(S\right)}$

Calculation:

Let S be all possible selections from 1, 2, .... 100.

$n\left(s\right) = 100$

A card is selected at random.

a. Let E be a card that is divisible by 5,

$E = \left\{5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100\right\}$

$n\left(E\right) = 20$

$P\left(E\right) = \frac{n\left(E\right)}{n\left(S\right)} = \frac{20}{100} = \frac{1}{5}$

To determine

To find:

b. What is the probability that the card selected either is a 1 or names a prime number?

Answer to Problem 25RE

b. $\frac{13}{50}$

Explanation of Solution

Given:

Each of the numbers 1, 2, ….. 100 is written on an index card, and the cards are shuffled. A card is selected at random.

Formula used:

$P\left(E\right) = \frac{n\left(E\right)}{n\left(S\right)}$

Calculation:

Let S be all possible selections from 1, 2, ….. 100.

$n\left(s\right) = 100$

A card is selected at random.

b. Let E be a card selected either is 1 or names a prime number.

$E = \left\{1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 83, 89, 97\right\}$

$P\left(E\right) = \frac{26}{100} = \frac{13}{50}$