Answer to Question #239578 in Statistics and Probability for Jenn

Question

If you randomly select a card from a well-shuffled standard deck of 52 cards, what is the probability that the card you select is a club or 7? (Your answer must be in the form of a reduced fraction.)

Answer 1

There are 13 club in a deck, so the probability to choose some club is

P(club) = 13/52 = 1/4.

There are 4 7 in a deck, so the probability to choose a 7 is

P(7) = 4/52 = 1/13.

The probability to choose the 7 of club is

P(7 of club) = 1/52.

Therefore,

P(club or 7) = P(club) + P(7) - P(7 of club) = 1/4 + 1/13 - 1/52 = 4/13

=0.308.

So, the probability that the card you select is a club or 7 is about .308.