College Algebra & Trigonometry, 2018a

332 CHAPTER 7. COMBINATORICS
The probability of getting at least two heads is 4 8 = 1 2
or 0.5
The probability of getting no heads is 1 8 =0.125
Example
A five-card poker hand is drawn from a standard deck of 52 cards. What is the
probability that all five cards are hearts?
The number of ways to draw five cards from a deck of 52 is 52 C 5 . This is a combination
since the order that the cards are drawn does not affect the outcome.
The number of ways of choosing 5 hearts from the 13 in the deck is 13 C 5 .
So the probability of drawing five hearts from a deck of 52 cards is 13 C 5
52C 5
=
1287
2598960 ≈ 0.000495
Example
A bag contains 20 tennis balls, of which four are defective. If two balls are drawn
at random from the bag, what is the probability that both are defective?
The sample space is the number of ways to choose two balls from the bag: 20C 2 .
Since there are 4 defective balls, the number of ways to draw two of them is 4 C 2 .
So, the probability that both balls will be defective is 4 C 2
20C 2
= 6
190 ≈ 0.0316.
We can also calculate the probability of drawing one defective ball:
4C 1 ∗ 16 C 1
20C 2
= 64
190 ≈ 0.3368.