The probability that a train leaves on time is 0.9. The probability that the train arrives on time and leaves on time is 0.36. What is the probability that the train arrives on time, given that it leaves on time?

1 Answer
Will
Aug 1, 2016

# .4#

Explanation:

Let #p(A)=.9# be the probability that a train leaves on time
#B# the event of arriving on time and we are given #p(A,B) = .36#

The question is what is #p(B|A)#.

we know that #p(A,B) = p(A|B)p(B)# or # p(B|A)p(A)#
if the two events are not independent otherwise its just the product of the two probabilities. Since it is not independent we use this fact to derive the results

#p(B|A) = (p(A,B))/(p(A)) = .36/.9 = .4#

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