# Card Probability Questions?

• Sep 24th 2012, 06:11 PM
allstar2
Card Probability Questions?
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:

b) The ace of spades of the queen of hearts?
c) An ace or a spade?
• Sep 25th 2012, 10:06 AM
Soroban
Re: Card Probability Questions?
Hello, allstar2!

This is a simple matter of Counting.

Quote:

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.

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

Quote:

What is the probability that you will draw:

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

Quote:

b) the Ace of Spades or the Queen of Hearts?
$\displaystyle P(A\spadesuit \vee Q\heartsuit) \:=\:\frac{2}{52} \:=\:\frac{1}{26}$

Quote:

c) an Ace or a Spade?
How many outcomes are "winners?

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

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