Quote: Im sorry, Im confused. Suppose the risk of any plane crashing is 1/5. You know that Joe will take 7 flights next year. What is the probability that Joe will die next year?
There isn't even close to enough information there. Do you mean the chance that any particular flight crashes is 20%, or that a plane crashes is 20%? How likely is a plane crash to be fatal? What other causes of death are there for Joe?
That said, let's assume that there is a 1/5 chance that a flight crashes, and we want to calculate the likelihood that at least one of the 7 flights that Joe is on will crash. It's easier to calculate the probability that none of them crashes, and subtract from 1. 1-(4/5)^7=61777/78125
So we come up with a plane crash about 3/4 of the time.