# Thread: Question on probabilities

1. Consider the following example:

1) The starting point is A
2)The probability to go from A to B is 3/5
3)The probability to go from A to C is 1/5
4)The probability to stay at A is 1/5
5)If you are at B you can never return to A
6)There is no direct way from B to C
7) There is an infinite number attempts to reach C

What is the probability of ever reaching point C?

i would suggest its 4/15, what do you think?

2.

3. The probability of staying at A after an infinite number of attempts is 0. You will either end up at B or C. The probability of going to B is 3 times the probabilty of going to C. So I think the answer is 0.25.

4. my idea was to splitt the 1/5 probability of remaining at point A in a ratio (1/5)/(4/5) and to add it to the 1/5 probability of reaching point C. you are right it is 0.25.

thanks harold

5. Originally Posted by Harold14370
The probability of staying at A after an infinite number of attempts is 0. You will either end up at B or C. The probability of going to B is 3 times the probabilty of going to C. So I think the answer is 0.25.
Correct, and nice reasoning.

Another way to reach the same conclusion is to model the process as a Markov chain and note that at each step the probbility of going to C is 1/5 and the probability of the chain going to another state from which C can be reached is also 1/5. So the probability of reaching C eventually is .

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