The probability that a person goes to college by car is 1 5 ; by bus 2 5 and by train is 3 5 respectively. The probabilities that he reaches the college late if he takes car, bus, train are 2 7 , 4 7 and 1 7 respectively. If he reaches the college in time, the probability that he traveled by car is

Step-by-step solution

Let C = The event that person goes by car B = The event that person goes by bus T = The event that person goes by train and L= The event that person reach as college late Now, P ( C )= 1 5 , P ( B )= 2 5 , P ( T )= 3 5 aligned & P ( L C )= 2 7 , P ( L B )= 4 7 , P ( L T )= 1 7 & and P ( L ^ C )= 5 7 , P ( L ^ B )= 3 7 , P ( L ^ T )= 6 7 aligned So, P ( C L^ )= P ( L^ C ) P(C) P ( L^ C ) P(C)+P ( L^ B ) P(B)+P ( L^ T ) P(T) = 5 7 1 5 5 7 1 5 + 3 7 2 5 + 6 7 3 5 = 5 5+6+18 = 5 29