Assume that a company hires employees on Mondays ,Tuesdays, Wednesdays with equa

Question

Assume that a company hires employees on Mondays ,Tuesdays, Wednesdays with equal likelihood. Complete parts? (a) through? (c) below. If two different employees are randomly? selected, what is the probability that they were both hired on a Wednesday? (A) & (B) is already answered.

A)The probability is__1/9______ ?(Type an integer or a simplified? fraction.) B) If two different employees are randomly? selected, what is the probability that they were both hired on the same day of the weekday of the week?? The probability is__1/3_____(Type an integer or a simplified? fraction.)

What is the probability that 66 people in the same department were all hired on the same
day of the weekday of the week?? Is such an event? unlikely? The probability is______
?(Type an integer or a simplified? fraction.)

Explanation / Answer

First we calculate the probability that 66 people were hired on same day, let's say monday.

Since a person can get hired on monday with probability 1/3, so the probability that all 66 were hired on monday = (1/3)^66

Since there are three weekdays, so this means that all 66 can get hired on monday, on tuesday or on wednesday as well.

So, the the probability that 66 people in the same department were all hired on the same
day of the weekday of the week = ((1/3)^66)*3 = (1/3)^65

This is approximately equal to zero. Yes this event is highly unlikely.

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