Question

You pick a card at random, put it back, and then pick another card at random. 6,7,8,9 What is the probability of picking a 9 and then picking an 8? Write your answer as a fraction or whole number.

Answer 1

We have that the probability to pick the card with 9 is:

$P(9)=\frac{1}{4}$

then, the probability of picking the card with 8 is:

$P(8)=\frac{1}{4}$

since we are replacing the card after picking the first card, both events are independent, then, we have:

$P(9\cap8)=P(9)\cdot P(8)=\frac{1}{4}\cdot\frac{1}{4}=\frac{1}{16}$

therefore, the probability of picking a 9 and then picking an 8 is 1/16