SOLUTION: Hi There, i'm doing some revision and I really can't figure these two questions out. I know I need to use the complement rule, but really don't get it. Help would be greatly apprec

Question 741202: Hi There, i'm doing some revision and I really can't figure these two questions out. I know I need to use the complement rule, but really don't get it. Help would be greatly appreciated on any aspects of any questions.

A university received 15 personal computers free from a new computer manufacturer as a method of trying the computers before placing a much larger order. Unknown to the university, 7 of these new computers are defective and will physically explode the first time they are turned on. Assume that you are the computer technician that has been assigned the task of setting up the first of these new computers. It is your job to set up 2 of the computers before you leave for the night. Assume that you have randomly selected two of the computers to set up. Find the probability that at least one of the computers that you selected will not explode when you turn them on.
(That is, find the probability that at least one of the two computers selected will work correctly when switched on.)
and
A human gene carries a certain disease from the mother to the child with a probability rate of 56%. That is, there is a 56% chance that the child becomes infected with the disease. Suppose a female carrier of the gene has three children. Assume that the infections of the three children are independent of one another. Find the probability that at least one of the children get the disease from their mother. Hint: Draw up a probability table where x the event is 'number of children who get disease'.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A university received 15 personal computers free from a new computer manufacturer as a method of trying the computers before placing a much larger order. Unknown to the university, 7 of these new computers are defective and will physically explode the first time they are turned on. Assume that you are the computer technician that has been assigned the task of setting up the first of these new computers. It is your job to set up 2 of the computers before you leave for the night. Assume that you have randomly selected two of the computers to set up. Find the probability that at least one of the computers that you selected will not explode when you turn them on.
(That is, find the probability that at least one of the two computers selected will work correctly when switched on.)
-----
Binomial Problem with n = and p(defective) = 7/15 ; p(good) = 8/15
----
P(1<= x <=2) = 1-P(x = 0) = 1-(7/15)^2 = 0.7822
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=====================

and
A human gene carries a certain disease from the mother to the child with a probability rate of 56%. That is, there is a 56% chance that the child becomes infected with the disease. Suppose a female carrier of the gene has three children. Assume that the infections of the three children are independent of one another. Find the probability that at least one of the children get the disease from their mother.
Binomial Problem with n = 3 and p(infected) = 0.56 ; p(not infected) = 0.44
P(1<= x <=3) = 1 - p(x = 0) = 1 - 0.44^3 = 0.9148
===================
Cheers,
Stan H.
Hint: Draw up a probability table where x the event is 'number of children who get disease'.

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