Chapter 13, Problem 39RE

To determine

To find: The probability that the number of the card is divisible by 5 and the selected number is either 1 or prime.

Answer to Problem 39RE

The probability that the card is of number divisible by 5 is 0.2, the probability that the card is 1 is 0.01 and the probability that number is both prime and 1 is 0.26.

Explanation of Solution

Given:

The number on card is from 1 to 100.

Calculation:

There are 20 number between 1 to 100 that are divisible by 5, so the sample space for this is,

  $n\left(s\right)=20$

Consider the probability of the event that the number on the card is divisible by 5 is 0.2 is,

  $\begin{array}{c}P\left(E\right)=\frac{20}{100}\\ =0.2\end{array}$

The probability for the event that the card selected from the sample space is 1 is,

  $\begin{array}{c}P\left(E\right)=\frac{1}{100}\\ =0.01\end{array}$

The number of prime numbers between 1 and 100 is 25, so the probability that the number is prime is,

  $\begin{array}{c}P\left(E\right)=\frac{25}{100}\\ =0.25\end{array}$

Consider the fact that the number is both prime and 1, then the probability is,

  $\begin{array}{c}P\left(E\right)=0.25+0.01\\ =0.26\end{array}$