Question

A card is selected from a standard deck of 52 playing cards.Find the probability that the card is a diamond or not a king?

I don't understand how to work it out.

Answer 1

`49/52 (~~.942)`

Explanation:

What you're trying to solve for is the `union` of `A` and `B`.

Let `A` be the probability of drawing a diamond, and let `B` be the probability of NOT drawing a king.

So, `P(A) = 13/52` (there are 13 diamonds in the deck), and `P(B) = 48/52` (there are 4 Kings in the deck, so there are `52-4=48` non-Kings).

The union of `P(A)` and `P(B)` is equal to `P(A) + P(B) - P(AnnB)`

The intersection (`AnnB`) is what `A` and `B` have in common.

What do `A` and `B` have in common? Basically, how many non-Kings are diamonds? Well, there are `12` non-King diamonds.

So, the probability of selecting a non-King diamond from the deck is `12/52`.

Thus, `P(AuuB) = P(A) + P(B) -P(AnnB) = 13/52+48/52-12/52`.

`P(AuuB) = 49/52`.