Question

A card is drawn at random from a standard 52–card deck. Find the probability that the card is neither an ace nor a heart.

Answer 1

First we want to find the probability that the card chosen is an ace or a heart.

That is to find, P(Ace OR Heart)

P(Ace OR Heart)

= P(Ace) + P(Heart) - P(Ace AND Heart)

= 4/52 + 13/52 - 1/52

= 16/52

= 4/13

P(Ace OR Heart) = 4/13

Now, we want find the probability that the card chosen is neither an ace nor a heart. That is to find, P(Ace OR Heart)^c

P(Ace OR Heart)^c = 1 - P(Ace OR Heart) = 1 - 4/13 = 9/13

P(Ace OR Heart)^c = 9/13 = 0.6923

Hence, the probability that the card is neither an ace nor a heart is 0.6923