Question

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.)

Answer 1

Answer:

Probability that at least one in 5 attempted call reaches the wrong number is 0.025

Explanation:

Let us define an event

E: The call is misdirected

then probability of the event E is

$P(E) = \frac{1}{200}$

Therefore,

$P(\bar E)=1-P(E)=1-\frac{1}{200}=\frac{199}{200}$

Probability that at least one in 5 attempted call reaches the wrong number

= 1 - Probability that no attempted call reaches the wrong number

$=1-(\frac{199}{200}\times \frac{199}{200}\times \frac{199}{200}\times \frac{199}{200}\times \frac{199}{200})$

$=1-(\frac{199}{200})^5$

$=7920399001/200^{5}$

$=0.025$

Answer 2

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 number

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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