Answer:
0.025
Step-by-step 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
= [tex]P(professor arrives at 8.21)/P(professor arrives after 8.20)\\= \frac{\frac{1}{60} }{\frac{40}{60} } \\=\frac{1}{40} \\=0.025[/tex]
