Question

1. a standard deck of cards contains 51 cards. one card is selected from the deck. compute the following probabilities: a. selecting a club or diamond. b. selecting a club or diamond or heart. c. selecting a five or spade.

Explanation:

Step1: Recall total number of cards

A standard deck has 52 cards.

Step2: Calculate probability for part a

There are 13 clubs and 13 diamonds. So the number of favorable outcomes for selecting a club or a diamond is $13 + 13=26$. The probability $P(A)=\frac{26}{52}=\frac{1}{2}$.

Step3: Calculate probability for part b

There are 13 clubs, 13 diamonds and 13 hearts. The number of favorable outcomes for selecting a club, diamond or heart is $13+13 + 13=39$. The probability $P(B)=\frac{39}{52}=\frac{3}{4}$.

Step4: Calculate probability for part c

There are 4 fives (one in each suit) and 13 spades. But the five - of - spades is counted twice. So the number of favorable outcomes for selecting a five or a spade is $4+13 - 1 = 16$. The probability $P(C)=\frac{16}{52}=\frac{4}{13}$.

Answer:

a. $\frac{1}{2}$
b. $\frac{3}{4}$
c. $\frac{4}{13}$