Question #b0568

1 Answer
Nov 21, 2017

4/13

Explanation:

Let us call A the event of drawing an Ace, and let us call B the event of drawing a Heart.

Since there are 4 Aces in a deck of cards, the probability of drawing an Ace is P(A) = 4/52 = 1/13. Since there are 13 Hearts in a deck of cards, the probability of drawing a Heart is P(B) = 13/52 = 1/4.

In a probability question such as this, the keyword "or" in the phrase "an ace or a heart" is synonymous with the union or addition of the probabilities of each of the mentioned events.

However, keep in mind that to properly calculate such a union of probabilities, you must account for the intersection of the events since you may be overcounting by simply adding the probabilities together. There's a handy formula that helps with this:

P(A uu B) = P(A) + P(B) - P(A nn B)

We know P(A) and we know P(B). What is P(A nn B)? This is the probability that you draw an Ace AND a Heart. Since there is only a single card in the deck which is both an Ace and a Heart, P(A nn B) = 1/52.

Thus:

P(A uu B) = 4/52 + 13/52 - 1/52 = 16/52 = 4/13