Question

. Aman has probability of 1/2 ,1/3 and 1/6 of choosing route A, B and C respectively from his house to the railway station .The choice of route is not influenced by weather. If weather is dry the probability of missing a train by routes A, B, and C are 1/20,1/10 and 1/5 respectively. He sent out on a dry day and missed the train, what is the probability that the route chosen was C?

Answer 1

Answer: The answer is $\dfrac{2}{55}.$

Step-by-step explanation:  Let us define the following events

X = the event that Aman chose route A,

Y = the event that Aman chose route B,

Z= the event that Aman chose route C,

S = the event of missing train by route A,

T = the event of missing train by route B

and

U = the event of missing train by route C.

So,

$P(X)=\dfrac{1}{2},~~P(Y)=\dfrac{1}{3},~~P(Z)=\dfrac{1}{6},~~P(S)=\dfrac{1}{20},~~P(T)=\dfrac{1}{10},~~P(U)=\dfrac{1}{5}.$

Therefore, the probability that Aman chosen the route C while he was out on a dry day and missed the train is given by

$p=\dfrac{P(Z)\times P(U)}{P(X)\times P(S)+P(Y)\times P(S)+P(Z)\times P(U)}\\\\\\\Righatrrow p=\dfrac{\dfrac{1}{30}}{\dfrac{1}{40}+\dfrac{1}{30}+\dfrac{1}{30}}=\dfrac{\dfrac{1}{30}}{\dfrac{110}{120}}=\dfrac{2}{55}.$

Thus, the required probability is $\dfrac{2}{55}.$

Answer 2

If in question Aman is equally like to choose one of the route a,b,c given then?

Probability is not given of choosing route then?

Please tell.