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?

Question

I don't understand how to work it out.

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Answer 1 · 2017-10-14T17:49:28

$49/52 (~~.942)$

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

$P(AuuB) = 49/52$ .