Question

A card is selected at random from a standard 52-card deck. (a) what is the probability that it is an ace? 4/52 (b) what is the probability that it is a heart? .25 (c) what is the probability that it is an ace or a heart

Answer 1

Part (a) is relatively straight forward.

There are 4 aces in a standard 52-card deck. So the probability that AN ace is picked is just 4/52.

Part (b):
Note that there are 4 suits in a standard 52-card deck. So picking hearts will be 13/52 or 1/4.

Part (c):
The probability condition OR means we need to add the two probabilities because we do not want them simultaneously. So, we end up getting Pr(ace) + Pr(heart).

From part (a), we found that picking an ace had a probability of 4/52, which is reduced down to 1/13.

From part (b), we found that picking a heart had a probability of 1/4.

So, the probability of an ace OR a heart is 1/13 + 1/4 = 4/52 + 13/52 = 17/52.