Probability on Bus Routes A, B & C: An Analysis

[Natasha1]

Well I wish Arildno but I have this last one to crack...

A town has three bus routes A, B and C. Route A has twice as many buses as each of B and C. Over a perido of time it has been found that, along a certain stretch of road, where the three routes converge, the buses on these routes run more than five minutes late 1/2, 1/5 and 1/10 of the time respectively.

1) A bus is going down this stretch of road. What is the probability it is more than 5 minutes late?

2) Comment on the size of the answer to 1) with the respect to the given probabilities 1/2, 1/5 and 1/10.

3) An inspector, standing on this particular stretch of road, sees a bus that is more than five minutes late. Find the probability that it is a route B bus.

Any help as I am very new to probabilities... thanks

 

[arildno]

Irrespective of the lateness of a bus observed on the common stretch, what is the probability that it came from A? From B? From C?

 

[Natasha1]

Irrespective of the lateness of a bus observed on the common stretch, what is the probability that it came from A? From B? From C?

So for 1) we have

p(more than 5 mins late) = 2/3 + 1/3 + 1/3 = 4/3

 

[arildno]

Not at all.
Try to answer my question first.

 

[Natasha1]

Irrespective of the lateness of a bus observed on the common stretch, what is the probability that it came from A? From B? From C?

from A is 2/3

from B is 1/3

from C is 1/3

 

[arildno]

Do those add up to one?

 

[Natasha1]

Do those add up to one?

would it be 1/3, 1/3 and 1/3 then?

 

[arildno]

No.
You know that there are twice as many buses on the A route as on either of the other two.

 

[Natasha1]

Do those add up to one?

2/3, 1/6 and 1/6

 

[arildno]

What is 2+1+1?

 

[0rthodontist]

Well, they added up to 1 that time but you do not have the right answer Natasha. Try making the situation more concrete. What if routes B and C have only one bus each? Then what would the probability be that a given bus comes from A, B, or C?