Question

Question #b0568

Answer 1

`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`