Let P(A) be the probability of using route A, P(B) be the probability of using route B, P(C) be the probability of using route C, P(M) be the probability of of missing a train.
Given P(A)=P(B)=P(C)=31
P(M∣A)=201,P(M∣B)=101,P(M∣C)=51
a.
The Law of Total Probability
P(M)=P(A)P(M∣A)+P(B)P(M∣B)
+P(C)P(M∣C)=31(201)+31(101)+51(31)
=601+2+4=607
b. The Multiplication Rule
P(C∩M)=P(C)P(M∣C)=
=31(201)=601
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