Ams 310 Survey Of Probability And Statistics Worksheet - Midterm Exam I - Stony Brook University Page 5
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11(3) Mechanical failure is accounted for 40 percent of airline accidents, the others are
due to human operation errors. Find the probability that in the next ten airline
accidents:
(a). None of them is due to human operation error.
(b). All of them are due to human operation error.
(c). Five of them are due to human operation error.
For each accident, it is a Bernoulli distribution with
. For 10
Solution:
p = 0.4
accidents, it is binomial distribution.
(a). All 10 are due to mechanical failur, so the probability is
10
10
10
B(x = 10; n = 10, p = 0.4) =
0.4
= 0.4
.
10
(b). None is due to mechanical failure,
10
10
10
B(x = 0; n = 10, p = 0.4) =
0.6
= 0.6
.
0
(c). Five are due to mechanical failure,
10
5
5
B(x = 5; n = 10, p = 0.4) =
0.4
0.6
.
5
5
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