Question

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?

Answer 1

Answer:

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<X<b)= proportion of the time considered / total time range = (a-b)/(c-d) , where c is the maximum time and d is the minimum one

then

P(4<X<5) = (5-4)/(11-3) = 1/8 = 0.125

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

P(X<6)= P(3<X<6) = (6-3)/(11-3) = 3/8 = 0.375

then using the theorem of Bayes

P( 4<X<5 | X<6 ) = P ( 4<X<5 ∩ X<6 ) / P(X<6) = P(4<X<5)/P(3<X<6) = 0.125 /0.375 = 1/3 (33.33%)

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%)