1. ## Probability Problem

there are two roads from A to B, and two roads from B to C.each of the four roads has independently probability 1/10 of being blocked by snow.What is the probability that one can drive from A to C?

2. ## Re: Probability Problem

Hi! We are glad that you posted here! This looks like a homework question though. Our homework help policy can be found here. We mainly just want to see what you have tried so far and that you have put some effort into the problem. I would also suggest checking out this thread for some guidelines on smart posting behavior that can help you get answers that are better much more quickly.

3. ## Re: Probability Problem

I have tried to solve it by tree diagram, and suggest that a union operations between the four roads. but unfortunately the resulted probabilities were larger than 1!!, can't any one give me a hint please?

4. ## Re: Probability Problem

If road 1 and road 2 lead from A to B, we need P(1 or 2). Similarly, if road 3 and road 4 lead from B to C we need P(3 or 4). Then, how do we use this info to get from A to C? (P(1 or 2) is the probably that one road or the other will take us there)

5. ## Re: Probability Problem

Thank you very much for your valuable hint.

6. ## Re: Probability Problem

You're welcome. There are a few approaches to this problem. One of them makes use of the complement rule. The probability that at least one road is open is... Try to figure it out this way and see if your two answers match.

7. ## Re: Probability Problem

Originally Posted by factstalk
Each road has a probability of 1/10 and since you have to take two roads then the answer is 1/5
This is wrong for more than one reason. By your logic if there were ten roads you needed to go down it would be guaranteed to be blocked.

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