Question

The arrival time of a professor to her office is uniformly distributed in the interval between 8 and 9 A.M. Find the probability that professor will arrive in the next minute given that she has not arrived by 8: 20.

Answer 1

0.025

Explanation:

Given that the arrival time of a professor to her office is uniformly distributed in the interval between 8 and 9 A.M.

If the professor did not arrive till 8.20 he will arrive between 8.21 and 8.40

Hence probability for arriving after 8.20 is 1/40

Prob he arrives at exactly 8.21 is 1/60

To find the probability that professor will arrive in the next minute given that she has not arrived by 8: 20.

= Prob that the professor arrives at 8.21/Prob he has not arrived by 8.20

This is conditional probability and hence

=
`P(professor arrives at 8.21)/P(professor arrives after 8.20)\\= ((1)/(60) )/((40)/(60) ) \\=(1)/(40) \\=0.025`