Question

you pick a card at random and put it back and then pick another card at random what is the probability of picking an even number and then picking a five

Answer 1

STEP - BY - STEP EXPLANATION

What to find?

The probability of picking an even number and then picking a five.

Given:

Step 1

State the probability formula.

$Probability=\frac{required\text{ outcome}}{all\text{ possible outcome}}$

Step 2

Identify the even numbers and the all possible outcome.

Even numbers =4, 6

Step 3

Find each of the probability.

Let A be the event of picking an even number and B be the event of picking a 5.

$\begin{gathered} P(A)=\frac{2}{4} \\ \\ P(B)=\frac{1}{4} \end{gathered}$

Step 4

Determine the compound probability.

$\begin{gathered} P(A\text{ and B\rparen=P\lparen A\rparen}\times P(B|A) \\ \\ =\frac{2}{4}\times\frac{1}{4} \\ \\ =\frac{2}{16} \\ \\ =\frac{1}{8} \end{gathered}$

Step 5

Convert to percentage.

$\begin{gathered} Probability=\frac{1}{8}\times\text{ 100\%} \\ \\ =12.5\text{ \%} \end{gathered}$

ANSWER

12.5 %