# Probability of bridge collapsing

1. Mar 8, 2009

### Sportsman4920

1. The problem statement, all variables and given/known data

Dystopia county has three bridges. In the next year, the Elder bridge has a 17% chance of collapse, the Younger bridge has a 6% chance of collapse, and the Ancient bridge has a 24% chance of collapse. What is the probability that exactly one of these bridges will collapse in the next year? (Round your answer to four decimal places.)

2. Relevant equations

3. The attempt at a solution

I thought the answer was the average of the 3 probabilities, which is 15.6666%. Then I realized that it would be the chance that each will collapse, not the chance that exactly one will collapse. However, I'm not sure what equation I need to use in order to find this. We've been using combinations and permutations in class, but I'm not sure if they are relevant for this problem.

Thanks

2. Mar 9, 2009

### Staff: Mentor

Re: probability

For exactly one bridge to collapse it must be true that the other two bridges don't collapse. So you have:
P(Elder bridge collapses AND Younger bridge doesn't collapse AND Ancient bridge doesn't collapse)
+ P(Elder bridge doesn't collapse AND Younger bridge does collapse AND Ancient bridge doesn't collapse)
+ P(Elder bridge doesn't collapse AND Younger bridge doesn't collapse AND Ancient bridge does collapse)

3. Mar 9, 2009

### Sportsman4920

Re: probability

Thanks a lot. I had been working on that one for a while.