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 14% 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. On Monday and again on Tuesday For the first time on Thursday Every day At least once during the week 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.)

Explanation / Answer

P(Interruption) = 0.14

SInce the interruption on any particular day will be independent from interruption from previous days:

a) P(Interruption on Monday and again on Tuesday) = (0.14)*(0.14) = 0.0196

b) P(Interruption for the first time on Thursday)

= P(No interruption on Monday, Tuesday and Wednesday) * P(Interruption on thursday)

= (0.86)3 * (0.14)

= 0.08905 (Rounded off to 5 decimal places)

c) P(Interruption every day) = (0.14)5 = 0.00005 (Rounded off to 5 decimal places)

d) P(At least once during the week)

= 1 - P(No interruption during the week)

= 1 - (0.86)5

= 0.52957 (Rounded off to 5 decimal places)

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