when mr shah goes from his office to his home ,he first takes either train or bus.The probability that he takes a train is 2/3 .After getting of the train he either takes a taxi or rickshaw to reach home . The probability that he takes a taxi is 1/4. If he travels by bus then after getting off the bus he either takes a rickshaw or walks to his home The probability that he walks is 2/5 Find the probability that he reaches home by rickshaw.
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T = event that he takes a train
B = event that he takes a bus = complement of T
R = event that he takes a rickshaw home.
We know that
P(T) = 2/3, P(B) = 1 - 2/3 = 1/3,
P(R given T) = 1 - 1/4 = 3/4, P(R given B) = 1 - 2/5 = 3/5.
The probability that he reaches home by rickshaw is
P(R) = P(R and T) + P(R and not T)
= P(R and T) + P(R and B)
= P(T)P(R given T) + P(B)P(R given B)
= (2/3)(3/4) + (1/3)(3/5)
= 7/10.
B = event that he takes a bus = complement of T
R = event that he takes a rickshaw home.
We know that
P(T) = 2/3, P(B) = 1 - 2/3 = 1/3,
P(R given T) = 1 - 1/4 = 3/4, P(R given B) = 1 - 2/5 = 3/5.
The probability that he reaches home by rickshaw is
P(R) = P(R and T) + P(R and not T)
= P(R and T) + P(R and B)
= P(T)P(R given T) + P(B)P(R given B)
= (2/3)(3/4) + (1/3)(3/5)
= 7/10.
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