Assume there are 23 homes in the Quail Creek area and 8 of t

Assume there are 23 homes in the Quail Creek area and 8 of them have a security system. Six homes are selected at random:

(a)

What is the probability all six of the selected homes have a security system? (Round your answer to 4 decimal places.)

(b)

What is the probability none of the six selected homes have a security system? (Round your answer to 4 decimal places.)

(c)

What is the probability at least one of the selected homes has a security system? (Round your answer to 4 decimal places.)

Solution

Assume there are 23 homes in the Quail Creek area and 8 of them have a security system. Six homes are selected at random:

n=6

P=8/23 =0.3478

Binomial distribution used

(a)

What is the probability all six of the selected homes have a security system? (Round your answer to 4 decimal places.)

P( x=6) = 0.0018

(b)

What is the probability none of the six selected homes have a security system? (Round your answer to 4 decimal places.)

P( x=0) =0.0770

(c)

What is the probability at least one of the selected homes has a security system? (Round your answer to 4 decimal places.)

P( x >=1) = 0.9230

Binomial Probabilities

Data

Sample size

6

Probability of an event of interest= 8/23 =

0.347826

Statistics

Mean

2.086957

Variance

1.3611

Standard deviation

1.1666

Binomial Probabilities Table

X

P(X)

0

0.0769

1

0.2462

2

0.3283

3

0.2335

4

0.0934

5

0.0199

6

0.0018