Question

5. Drawing a Card: If a card is drawn from a deck, find the probability of 

getting these results: 

a. A 6 and a spade 

b. A black king 

c. A red card and a 7 

d. A diamond or a heart 

e. A black card

Answer 1

The probability formula:

$P(\text{event})=\frac{\text{number of favorable outcomes}}{\text{total number of outcomes}}$

We have 52 card in a deck, so the total number of outcomes is 52.

a. There is one card in a deck that is  a 6 and a spade, so

$P( \text{getting a 6 and a spade})=\frac{1}{52}.$

b. There are two black kings in a deck (a club king and a spade king), so

$P( \text{getting a black king})=\frac{2}{52}=\frac{1}{26}.$

c. There are two red 7s in a deck (a heart 7 and a diamond 7), so

$P( \text{getting a red card and a 7})=\frac{2}{52}=\frac{1}{26}.$

d. There are 13 diamonds and 13 hearts in a deck, so

$P( \text{getting a diamond or a heart})=\frac{26}{52}=\frac{1}{2}.$

e. There are 26 black cards in a deck (13 clubs and 13 spades), so

$P( \text{getting a black card})=\frac{26}{52}=\frac{1}{2}.$