Answer to Question #171616 in Statistics and Probability for Mohsin ali

Question

i. Ali starts driving for office in the morning at sometime uniformly chosen in the interval [8:30,9.00]. a) What is the probability that he starts driving before 8:45? b) His favorite radio program comes on at 8:30 and may last anywhere between 5 to 15 minutes with equal probability. What is the probability that he catches at least a part of the program?

Answer 1

1. Because time is uniformly distributed, the probability that he starts driving before 8:45 is equal to the time interval favorable for event divide to the time interval of a whole time. The probability is 15/30 = 1/2

Let X is random variable which means the time when Ali starts driving after 8:30 (if time is 8:35, then X = 5), Y is random variable which means the time when program last after 8:30. So X is uniformly distributed on [0;30] and Y is uniformly distributed on [5;15]. We need to find P(X <= Y/2 ) = blue square / red square. It's valid because of uniform distribution. Hence P(X <= Y/2 ) = (15*7.5/2) / (30*15) = 1/8