Respuesta :
Answer:
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.
[tex]P(X \leq x) = \frac{x - a}{b-a}[/tex]
Probability that you miss the first friend:
Somewhere between 12 and 12:30 pm, so his lunches are between 0 and 30 minutes, so [tex]a = 0, b = 30[/tex]
You arrive at 12:20. So if his lunch is 20 or less minutes, you miss him.
[tex]P_{1} = P(X \leq 20) = \frac{20 - 0}{30 - 0} = 0.6667[/tex]
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 [tex]a = 0, b = 30[/tex].
You arrive at 12:20. So if his lunch is 5 or less minutes, you miss him.
[tex]P_{2} = P(X \leq 20) = \frac{5 - 0}{30 - 0} = 0.1667[/tex]
Probability that you miss both friends:
Missing the first friend and the second friend are independent events. So we multiply these probabilities.
[tex]p = P_{1}*P_{2} = 0.6667*0.1667 = 0.1111[/tex]
11.11% probability that you have missed both friends in the cafeteria
