An important part of the customer service responsibilities of a cable company relates to the speed with which trouble in service can be repaired. Historically, the data show that the likelihood is 0.75 that troubles in a residential service can be repaired on the same day. For the first five troubles reported on a given day, what is the probability that: Fewer than two troubles will be repaired on the same day? a. 0.6328b. 0.0010c. 0.0156d. 0.0146

Question

Mathematics

Trace

5 September, 16:36

An important part of the customer service responsibilities of a cable company relates to the speed with which trouble in service can be repaired. Historically, the data show that the likelihood is 0.75 that troubles in a residential service can be repaired on the same day. For the first five troubles reported on a given day, what is the probability that: Fewer than two troubles will be repaired on the same day? a. 0.6328b. 0.0010c. 0.0156d. 0.0146

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Fields · Answer 1

0.0156

Step-by-step explanation:

Given X~Binomial (n=5, p=0.75)

x = number of trials

P (X=x) = xC_5 * (0.75^x) * (0.25^ (5-x))

So the probability is

P (X<2) = P (X=0) + P (X=1)

=0C_5 * (0.75^0) * (0.25^ (5-0)) + 1C_5 * (0.75^1) * (0.25^ (5-1))

=0.015625

Answer:0.0156