One of your friends eats lunch in the cafeteria sometime between 12:00 P. M. And 12:30 P. M. Another friend eats lunch in the cafeteria sometime between 12:15 P. M. And 12:45 P. M. Today you get to the cafeteria at 12:20 P. M. What is the probability that you have missed both friends in the cafeteria?.

11.11% probability that you have missed both friends in the cafeteria

Step-by-step explanation:

We use the uniform probability distribution to solve this question, since each lunch duration is equally as likely.

Uniform distribution:

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The probability that we find a value X lower than x is given by the following formula.

Probability that you miss the first friend:

Somewhere between 12 and 12:30 pm, so his lunches are between 0 and 30 minutes, so

You arrive at 12:20. So if his lunch is 20 or less minutes, you miss him.

Probability that you miss the second friend:

Somewhere between 12:15 and 12:45 pm, so his lunches are between 0 and 30 minutes, so .

You arrive at 12:20. So if his lunch is 5 or less minutes, you miss him.

Probability that you miss both friends:

Missing the first friend and the second friend are independent events. So we multiply these probabilities.

11.11% probability that you have missed both friends in the cafeteria

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step-by-step explanation:

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