A company has recently replaced their e-mail server because previously mail was

Question

A company has recently replaced their e-mail server because previously mail was interrupted on about 15% of workdays. To see how bad the situation was, calculate the probability that during a 5-day work week, there would be e-mail interruptions as described in parts a through d.

a) The probability that there would be an e-mail interruption on Monday and again on Tuesday is ?.

(Type an integer or decimal rounded to five decimal places as needed.)

b) The probability that there would be an e-mail interruption for the first time on Thursday is ?.

(Type an integer or decimal rounded to five decimal places as needed.)

c) The probability that there would be an e-mail interruption every day is ?.

(Type an integer or decimal rounded to five decimal places as needed.)

d) The probability that there would be an e-mail interruption at least once during the week is ?.

(Type an integer or decimal rounded to five decimal places as needed.)

Explanation / Answer

If it's 15% (0.15) of the workdays that have email interruptions, then we can do these.

a. Two given days: 0.15 * 0.15 = 0.0225

b. first time on Thursday (0.85)

0.85 * 0.15 = 0.1275

c. Five specified days (as it happens, in a row):
0.15^5 = 0.0000759375

d. If there's an interruption on at least one day, then there's NOT five interruption-free days. The probability of one day being interruption-free is 85%, so the probability of all five days being interruption-free is
0.85^5 = 0.4437053125

The probability of that (or any other event) NOT occurring is obtained by subtracting its probability from certainty (1).
1 - 0.4437053125 = 0.5562946875

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