Solutions to Exercises 5
1. We are told that the product fails if any of A,Bor Cfail. Therefore
(a)
P r(A, B, C all last for at least a year)
=P r(Alasts for at least a year AND Blasts for at least a year AND Clasts for at least a year)
=P r(Alasts for at least a year)×P r(Blasts for at least a year)×P r(Clasts for at least a year)
assuming the components fail independently, and so
P r(A, B, C all last for at least a year) = 0.98 ×0.99 ×0.95 = 0.92169.
(b)
P r(product is returned for a refund) = 1 −P r(product is not returned for a refund)
= 1 −P r(A, B , C all last for at least a year)
= 1 −0.92169
= 0.07831.
2. (a) There are 4 female students out of 18. So the probability that the student is female is
4
18 = 0.2222.
(b) There are 6 students with weights greater than 70kg. So the probability that the stu-
dent’s weight is greater than 70kg. is
6
18 = 0.3333.
(c) There are 4 students with weights greater than 70kg. and shoe-sizes greater than 8. So
the probability of choosing such a student is
4
18 = 0.2222.
(d) There are 8 students with weights greater than 70kg. or shoe-sizes greater than 8. So
the probability of choosing such a student is
8
18 = 0.4444.
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