CK-12 Basic Probability and Statistics - A Short Course

3.1. Discrete Random Variables http://www.ck12.org

9.P(4 heads)= 256 =24%

10.

#o f favorable choices=

12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

( 4 × 3 × 2 × 1 )×( 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 )

#o f favorable choices=

479001600

( 24 )×( 40320 )

#o f favorable choices=

479001600

967680

#o f favorable choices= 495

The number of possible outcomes= 212 The number of possible outcomes=4096 Now we just divide the

numerator by the denominator.

P( 4 heads) =

495

4096

P( 4 heads) = 0. 121

P(8 heads) = 19 .7%

11.P(8 heads) = 4 .39%

12.

#o f favorable choices=

15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

( 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 )×( 7 × 6 × 5 × 4 × 3 × 2 × 1 )

#o f favorable choices=

1. 31 × 1012

( 40320 )×( 5040 )

#o f favorable choices=

1. 31 × 1012

203212800

#o f favorable choices= 6446

The number of possible outcomes= 215 The number of possible outcomes=32768 Now we just divide the

numerator by the denominator.

P( 8 heads) =

6446

32768

P( 8 heads) = 0. 197

P(8 heads) = 19 .7%

Answer Key for Review Questions (even numbers)