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 select another card. What is the probability that the first card is an even number and the second card is greater than 6?
Write your answer as a fraction in simplest form.

Answer 1

Four of the cards have an even number, so the probability of drawing an even is $\dfrac48=\dfrac12$.

Only two cards have a number greater than 6 (7 and 8), so the probability of drawing one of them is $\dfrac28=\dfrac14$.

The probability of both events happening is

$\dfrac12\times\dfrac14=\dfrac18$