Question

There is a stack of 8 cards, each given a different number from 1 to 8. Suppose we select a card randomly from the stack, replace it, and then randomly selectanother card. What is the probability that the first card is an even number and the second card is less than 4?Write your answer as a fraction in simplest form.

Answer 1

3/16

Step-by-step explanation:

The total number of cards = 8

There are 4 even numbers in the stack: {2,4,6,8}

`P(\text{the first card is an even number)}=(4)/(8)`

The number of cards less than 4,{1,2,3} =3

`P(\text{second card is less than 4)}=(3)/(8)`

Therefore, the probability that the first card is an even number and the second card is less than 4:

`\begin{gathered} =(4)/(8)*(3)/(8) \\ =(1)/(2)*(3)/(8) \\ =(3)/(16) \end{gathered}`