Question

A boss plans a business meeting at Starbucks with the two engineers below him. However, he fails to set a time, and all three arrive at Starbucks at a random time between and p.m. When the boss shows up, if both engineers are not already there, he storms out and cancels the meeting. Each engineer is willing to stay at Starbucks alone for an hour, but if the other engineer has not arrived by that time, he will leave. What is the probability that the meeting takes place

Answer 1

The probability that the meeting takes place is 7/24.

What is the probability?

Probability is defined as the ratio of the number of favorable outcomes of an event to the total number of possible outcomes(sample space) of the event.

It is given by

P(A) = n(A)/n(S)

Where A - event, S - sample space

Calculation:

From the given data,

The probability, if the engineers arrive in the first hour and the boss arrives in the second hour is 1/8,

So, the meeting will be held i.e., p = 1.

The probability, if all the three arrive in the same hour (first or second)

= 1/8 + 1/8

= 1/4

So, the meeting will be held only if the boss (he may arrive first, second, or last) arrives last, the probability is 1/3

The probability, if one of the engineers arrives in the first hour while the other engineer and the boss arrive in the second hour is

= 1/4

So, the meeting will be held only if the second engineer arrives before the boss and before the first engineer leaves, the probability is 1/3

Thus, the final probability for the meeting to take place is

= (1/8) × 1 + (1/4) × (1/3) + (1/4) × (1/3)

= 7/24

Therefore, the required probability is 7/24.

Learn more about the probability here:

https://brainly.com/question/251701

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