Geometry Homework

Question

In a standard deck of cards, what is the probability of picking a red card or a face card, when choosing at random?

A. 4/13

B. 8/13

C. 9/13

D. 7/13

Answer 1

We have to do 3 calculations:

1) The probability of picking a red card, half the deck is red so Probability = 1/2

2) The probability of picking a face card, there are 3 face cards per suit (4 suits: hearts, spades, etc.). So probability = (12/52) = 3/13

So since it's and "OR" question, we add the probabilities together. 1/2 + 3/13 = 13/26 + 6/26 = 19/26.

BUT WAIT, some cards are BOTH RED AND FACE CARDS! So we double counted those, so we can to subtract them. There are 6 red face cards: 6/52 = 3/26

So let's subtract (so we don't double count) and get our final answer: 19/26 - 3/26 = 16/26 = 8/13

B)

Answer 2

We luking for P(RUF) = P(R) + P(F) - P(R∩F0

R is event "we pick red card" and F is event "we pick face card"

P(R) = 26/52 = 1/2, P(F) = 12/52 = 3/13; P(R∩F) = 6/52 = 3/26

So, P(R∪F) = 1/2 +3/13 - 3/26 = 8/13