Card Probability Questions?

**allstar2** · September 24th 2012, 06:11 PM

Suppose you have a deck of 52 cards. You are to draw one card. Assume each card has a probability of 1/52 of being drawn. What is the probability that you will draw:

a)The ace of spades?
b) The ace of spades of the queen of hearts?
c) An ace or a spade?

**Soroban** · September 25th 2012, 10:06 AM

Hello, allstar2!

This is a simple matter of Counting.
Exactly where is your difficulty?

Suppose you have a deck of 52 cards. .You are to draw one card.
Assume each card has a probability of 1/52 of being drawn.

$P(\text{any particular card}) \:=\:\frac{1}{52}$

What is the probability that you will draw:

a) the Ace of Spades?

$P(A\spadesuit) \:=\:\frac{1}{52}$

b) the Ace of Spades or the Queen of Hearts?

$P(A\spadesuit \vee Q\heartsuit) \:=\:\frac{2}{52} \:=\:\frac{1}{26}$

c) an Ace or a Spade?

How many outcomes are "winners?

$A\heartsuit,\,A\clubsuit,\,A\diamondsuit,\,A \spadesuit,\,2\spadesuit,\,3\spadesuit,\,4 \spadesuit,\,5\spadesuit,\,6\spadesuit,\,7 \spadesuit,\,8\spadesuit,\,9\spadesuit,\,10 \spadesuit,\,J\spadesuit,\,Q\spadesuit,\,K \spadesuit$
. . (16 outcomes)

Therefore: . $P(A \vee \spadesuit) \:=\:\frac{16}{52} \:=\:\frac{4}{13}$

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