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Assume there are 22 homes in the Quail Creek area and 7 of them have a security

ID: 3219429 • Letter: A

Question

Assume there are 22 homes in the Quail Creek area and 7 of them have a security system. Five homes are selected at random:

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

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

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

Assume there are 22 homes in the Quail Creek area and 7 of them have a security system. Five homes are selected at random:

Explanation / Answer

22 homes

7 homes have security system ,15 homes don't have security system

a)

Total no of ways to selct 5 homes from 22 = 22C5 = 26334

no of ways to select 5 homes from 7 securtiy homes = 7C5 = 21

a)probability that all five of the selected homes have a security system

= no of ways to select 5 homes from 7 securtiy homes/Total no of ways to selct 5 homes from 22

= 21/26334 = 0.0008

b)

no of ways to select 5 homes from 15 non securtiy homes = 15C5 = 3003

probability that none of the five selected homes has a security system

= no of ways to select 5 homes from 15 non securtiy homes/Total no of ways to selct 5 homes from 22

= 3003/26334 =0.11403 ~ 0.1140

c)

probability at least one of the selected homes has a security system = 1-probability that none of the five selected homes has a security system = 1-3003/26334 = 0.88596 ~ 0.8860