Ten Very Important People

Probability Level 4

10 people each think they are very important, and they have a daily meeting arranged at 10AM.

Once everyone has arrived, the meeting starts.

However, each one thinks they are so important that they must arrive last (or at least at the same time as the last person), so they shoot for whatever time the last person arrived last time they had a meeting.

Each person has a $\dfrac{1}{10}$ probability of arriving 1 minute late, otherwise, they will arrive on the time they are shooting for (the time that the last person arrived at the last meeting).

What is the expected number of meetings, until the meeting starts 5 minutes late, at 10:05AM?

Give your answer to 2 decimal places.

Image credit: https://businessfirstfamily.com

The answer is 7.68.

1 solution

Geoff Pilling
Nov 5, 2016

Every meeting, the probability that everyone gets there on time is:

$p = (\frac{9}{10})^{10}$

So, the probability that one person will be late is given by $1-p$ .

So, every meeting, the expected time slip is $1-p$

Therefor the number of meetings in order for the time slip to be 5 minutes will be $\frac{5}{1-p} = \boxed{7.68}$

Ten Very Important People

The answer is 7.68.

1 solution

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