MHB What Is the Probability a Random Road Choice Leads to the Factory?

[onika]

There are four road junctions labelled A,B,C,D and four towns labelled W,X,Y,Z,. Driver is approaching junction A from Town W, when he realizes that he does not know how to get to the factory. He decides that at road junction he will choose a road to take random , but he will not go back to the road he just traveled from.

a) write down the probability that driver will choose the direct road to the factory at road junction A.

ans: 1 by 3

b) show the probability that driver will pass through excatly two road junctions andreach the factory is 5 by 18.

I don't really know this one

 

[I like Serena]

Re: probability

There are four road junctions labelled A,B,C,D and four towns labelled W,X,Y,Z,. Driver is approaching junction A from Town W, when he realizes that he does not know how to get to the factory. He decides that at road junction he will choose a road to take random , but he will not go back to the road he just traveled from.

a) write down the probability that driver will choose the direct road to the factory at road junction A.

ans: 1 by 3

b) show the probability that driver will pass through excatly two road junctions andreach the factory is 5 by 18.

I don't really know this one

Hi onika! Welcome to MHB! ;)

I'm not exactly clear on the road layout.
Can you clarify?

I'm assuming the factory is in one of the cities. Is that the case?

From the problem statement it appears there is a direct road to the factory from junction A.
If so, the driver could backtrack after each wrong choice and try again.
But in that case, the probability would be 2/3 to first take a wrong road, and then 1/2 to take the right road, giving us a probability of $\frac 23 \cdot \frac 12 = \frac 13$, so that doesn't seem to be the case after all.
How do the other junctions B,C,D tie in?