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:

a)The ace of spades?

b) The ace of spades of the queen of hearts?

c) An ace or a spade?

Re: Card Probability Questions?

Hello, allstar2!

This is a simple matter of Counting.

Exactly where is your difficulty?

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:

a) the Ace of Spades?

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

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