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)=(2)/(4) \\ \\ P(B)=(1)/(4) \end{gathered}`

Step 4

Determine the compound probability.

`\begin{gathered} P(A\text{ and B\rparen=P\lparen A\rparen}* P(B|A) \\ \\ =(2)/(4)*(1)/(4) \\ \\ =(2)/(16) \\ \\ =(1)/(8) \end{gathered}`

Step 5

Convert to percentage.

`\begin{gathered} Probability=(1)/(8)*\text{ 100\%} \\ \\ =12.5\text{ \%} \end{gathered}`

ANSWER

12.5 %