4. AT&T was running commercials in 1990 aimed at luring back customers who had switched to one of the other long-distance phone service providers. One such commercial shows a businessman trying to reach Phoenix and mistakenly getting Fiji, where a half-naked native on a beach responds incomprehensibly in Polynesian. When asked about this advertisement, AT&T admitted that the portrayed incident did not actually take place but added that this was an enactment of something that “could happen.” Suppose that one in 200 long-distance telephone calls is misdirected. What is the probability that at least one in five attempted telephone calls reaches the wrong number? (Assume independence of attempts.)
Answers
Given : one in 200 long-distance telephone calls is misdirected.
To find : probability that at least one in five attempted telephone calls reaches the wrong numbe
Solution:
one in 200 long-distance telephone calls is misdirected
=> probability of call misdirecting p = 1/200
Probability of call not Misdirecting = 1 - 1/200 = 199/200
Number of Calls = 5
P(x) = ⁿCₓpˣqⁿ⁻ˣ
n = 5
p = 1/200
q = 199/200
at least one in five attempted telephone calls reaches the wrong number
= 1 - none of the call reaches the wrong number
= 1 - P(0)
= 1 - ⁵C₀(1/200)⁰(199/200)⁵⁻⁰
= 1 - (199/200)⁵
= 0.02475
probability that at least one in five attempted telephone calls reaches the wrong number = 0.02475
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