Chapter 11, Problem 1T

Numbers from Sets of Digits Two numbers are randomly selected without replacement from the set {1, 2, 3, 4, 5}.

Find the probability of each event.

Both numbers are even.

To determine

To Calculate: Probability of the event that both numbers are even when 2 numbers are randomly selected without replacement from the set $\left\{1,2,3,4,5\right\}$.

Answer to Problem 1T

Solution:

Probability is:$\frac{1}{10}$.

Explanation of Solution

Given:

Two numbers are randomly selected without replacement from the set $\left\{1,2,3,4,5\right\}$.

Formula Used:

$P\left(\text{Both numbers are even}\right)=P\left(A\right)\times P\left(B\right)$

Where,

$A:$ First number drawn is even.

$B$: Second number drawn is even.

Calculation:

Even numbers in the provided set are $2\text{ and }4$ and total numbers in the set are $5$. Consider the events,

$A:$ First number drawn is even.

$B$: Second number drawn is even.

It is provided that numbers are drawn without replacement. So, probability of the event that both numbers are drawn even without replacement is:

$\begin{array}{c}P\left(\text{Both numbers are even}\right)=P\left(A\right)\times P\left(B\right)\\ =\frac{2}{5}\times \frac{1}{4}\\ =\frac{1}{10}\end{array}$

The probability of the event that both numbers are drawn are even is: $\frac{1}{10}$.