LSSGB: Find the Probability

The probability of a train arriving on time and leaving on time is 0.8. The probability of the same train arriving on time is 0.84. The probability of this train leaving on time is 0.86. Given the train arrived on time, what is the probability it will leave on time?

Options

• 0.93
• 0.84
• 0.88
• 0.95

Answer

0.95

EXPLANATION

The solution to this problem involves conditional probability. The probability of event B occurring, given event A has occurred, is: Let event B be the probability the train leaves on time, and let event A be the probability of the train arriving on time. The intersection of events A and B is the probability of the train arriving and leaving on time. Thus, the probability of event B given event A has occurred is 0.8/0.84 = 0.9524.