A man can go from A to B by road X or Y. The chance of a traffic jam on X is 1/5 and on Y is 1/8. If he is twice as likely to go by X as Y, chance he will hit a traffic jam is?

Question

A man can go from A to B by road X or Y. The chance of a traffic jam on X is 1/5 and on Y is 1/8. If he is twice as likely to go by X as Y, chance he will hit a traffic jam is>?

crashonce · Answer

ye

crashonce · Answer

can u help with this one

anonymous · Answer

Basically, add the probability of each outcome that would lead to a traffic jam.
One way is that he goes on X and gets into a traffic jam

anonymous · Answer

The other way is he goes on Y and gets into a traffic jam.

anonymous · Answer

The probability of a road having a traffic jam is independent of whether he takes it or not.

anonymous · Answer

@CrashOnce Does this help at all?

crashonce · Answer

im not sure what u mean

anonymous · Answer

What is the probability he takes road X and that he gets into a traffic jam on road X?  Can you figure that out?

anonymous · Answer

Using: $$
\Pr(A\cap B) = \Pr(A)\cdot \Pr(B)
$$since they are independent events.

anonymous · Answer

1.  What is the probability he will take road X?

crashonce · Answer

sorry i dont get it can u explain simnpler

anonymous · Answer

"he is twice as likely to go by X as Y"

anonymous · Answer

He is only going to take one road or the other...

anonymous · Answer

If $y$ represent the probability he takes road Y, then $2y$ is the probability he takes road X.  He must take one road or the other, so the probabilities must add up to one.
This means:$$
y+2y = 1\implies 3y=1\implies y=\frac 13
$$So the probability he takes Y is $1/3$ and t he probability he takes X is $2/3$.

anonymous · Answer

But you aren't going to even try are you?

anonymous · Answer

Do you expect me to just give you an answer?  I mean what do you know?

perl · Answer

The probability of picking road X is 2 times the probability of picking road Y 

Let P(Y) = k  

then 

P(X) = 2*P(Y) 

by substitution this gives us

P(X) = 2*k 


since X and Y are complementary events (either you can go on road X or road Y, and must do one or the other , and can't do both)

P(X) + P(Y) = 1 

2k + k = 1 

3k = 1 
k  = 1/3 

therefore 

P(X) = 2/3

P(Y) = 1/3

We are not done though...

perl · Answer

can you solve it now?

anonymous · Answer

I think 8/13. 
Am I right?

crashonce · Answer

@wio  i had to go so i couldnt answer you, please try not to be so rude