Question

Based on a study from the Chronicles of Flippin'' Awesomeness, the probability that Napoleon and Pedro make it to their first period class on time is 0.20. The probability that they make it to their first period class on time, given that they catch the bus is 0.73. The probability that Napoleon and Pedro catch the bus and make it to their first period class on time is 0.47. What is the probability that Napoleon and Pedro catch the bus?

Answer in decimal form. Round to 4 decimal places as needed.

Answer 1

Solution :

Let A be the event that Napoleon and Pedro make it to their 1st period and let B be the event that they catch the bus.

Given, P(Napoleon and Pedro make it to their 1st period) =P(A) =0.20.

P(they catch the bus given that they make it to their 1st period) =P(B l A) =0.47

P(AB)/P(A) =0.47

P(AB) =0.47*0.20=0.094[since P(A) =0.20]

P(they make it to their 1st period given that they catch the bus) =P(A l B) =0.73

P(AB) /P(B) =0.73

0.094/0.73=P(B)

P(B) =0.128767(approximately)

Thus, the probability that they catch the bus is=0.1288

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