The amount of time it takes Michelle to make a grilled cheese sandwich is continuous and uniformly distributed between 3 minutes and 11 minutes. What is the probability that it takes Michelle between 4 and 5 minutes given that it takes less than 6 minutes for her to make a grilled cheese sandwich?

Question

Mathematics

Kemp

21 June, 14:57

The amount of time it takes Michelle to make a grilled cheese sandwich is continuous and uniformly distributed between 3 minutes and 11 minutes. What is the probability that it takes Michelle between 4 and 5 minutes given that it takes less than 6 minutes for her to make a grilled cheese sandwich?

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Answers (1)

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Amaya Stokes · Answer 1

the probability that takes between 4 and 5 minutes to make the sandwich is 1/3 (33.33%)

Step-by-step explanation:

since the random variable X = time taken to make a grilled cheese sandwich is uniformly distributed, then the probability is governed by

P (a
then

P (4
since we already know that takes less than 6 minutes, then

P (X<6) = P (3
then using the theorem of Bayes

P (4
therefore given that we already know that will take Michelle less than 6 minutes, the probability that takes between 4 and 5 minutes to make the sandwich is 1/3 (33.33%)