Bmat 2019, question 20

Practice Question Solving
,
1

To get to work, Sylvie first catches a bus and then catches a train.

The probability that the bus is on time is 0.6

The probability that the bus is late is 0.4

If the bus is on time, then the probability that she will catch the train is 0.8

If the bus is late, then the probability that she will catch the train is 0.6

Given that Sylvie catches the train, what is the probability that the bus was on time?

the answer is 2/3

2

hi

the easiest way to visualize the question is to draw a probability tree

using the probability equation
P(A knowing B) = (P(B knowing A) * P(A)) / P(B)

P(bus on time knowing she caught the train) = (P(caught the train knowing the bus was on time) * P(bus on time) / P(catches the train)

= (0,6 * 0,8) / (0,6 * 0,8 + 0,4 * 0,6) = 4,8/7,2 = 2/3