When you haven't crossed the road yet, it's more probable to die the 1st time you cross it than to die on the 2nd time.

However, once you have crossed the road one time, and survived, now, the probability of you getting hit the next time just went up a little. Just because you survived the 1st one.

abc, I'm looking at your

" EDIT: There are 101 cases, but each crash case has a different probability to occur

first case: 1/100

second case: 99/100*1/100*

third case:99/10099/100*1/100

and still goes…the total is the probability

I am not sure if that's the answer, I am into it now, please post any suggestions!"

It's ok, and you can prove that you get the same result as gorlom.

However it's not a good way to quickly get an intelligible answer :

According to that logic, the probability that you get hit while crossing the road is

P = 1/100 + 99/100*1/100 + 99/100*99/100*1/100 + ...... + (99/100)^99 * 1/100.

It's a big sum with 100 different terms. So I hope you are not planning to enter it into a calculator like that.

Now look at 99/100 * P :

99/100*P = 99/100*1/100 + 99/100*99/100*1/100 + ...... + (99/100)^99 * 1/100 + (99/100)^100 * 1/100.

It looks almost the same as P :

99/100*P = P - 1/100 + (99/100)^100 * 1/100.

When you solve this little manageable equation, you eventually get

P = 1 - (99/100)^100, which is what was answered right from the start.

The probability of being hit is 1 minus the probability of never being hit any of the 100 times you cross the road , thus is 1 - (99/100)^100.

which is WAY EASIER to get a hold of than doing the tedious sum of the probabilities of being hit for each time you cross the road.