Assume there are 20 homes in the Quail Creek area and 10 of

Assume there are 20 homes in the Quail Creek area and 10 of them have a security system. Six homes are selected at random:

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

What is the probability none of the six 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.)

Solution

a)

There are 20C6 ways to choose 6 homes.

There are 10C6 ways to choose 6 with security system.

Thus,

P(all 6 has security) = 10C6 / 20C6 = 0.005417957 [ANSWER]

*******************

b)

There are 20C6 ways to choose 6 homes.

There are 10C6 ways to choose 6 without security system.

Thus,

P(all 6 has no security) = 10C6 / 20C6 = 0.005417957 [ANSWER]

***********************

c)

P(at least one has security) = 1 - P(all have no security)

= 1 - 0.005417957

= 0.994582043 [ANSWER]

*******************

d)

They are dependent, as the probability of the next one having security is updated everytime we pick one home. [ANSWER, DEPENDENT]