An Apple call center keeps track of whether there was an actual problem with the

Question

An Apple call center keeps track of whether there was an actual problem with the hardware, meaning the computer has to be taken to an Apple Store to be fixed, or whether the problem can be fixed over the phone. Of the past 60 calls, 38 were able to be fixed over the phone and 22 were problems with the hardware. A supervisor is taking a random sample of 6 calls.

a. In how many ways can the sample of 6 be selected so that exactly 4 had to be sent to the store for repair?

b. Considering a random sample of 6 calls, what is the probability that all six can be resolved over the phone?

Explanation / Answer

(a) 4 calls can be selected from 22 calls in C(22, 4) ways = 7315 ways and 2 calls can be selected from 38 calls in C(38, 2) ways = 703 ways

So, number of ways = 7315 * 703 = 5142445 ways

(b) 6 calls can be selected from 38 calls in C(38, 6) ways = 2760681 ways

6 calls can be selected from 60 calls in C(60, 6) ways = 50063860 ways

Probability = 2760681/50063860 = 0.055

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