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