ELi5 Probability odds help. Im not math genius 15% chance 3 times but if I hit on any of those chances I get the whole thing

Question

So I have a math probablity question.

Lets say there is a pile of money that I can win. I get 15 random numbers assigned to me (i get no say in the matter) and then a number out of 100 is drawn at random. If I hit on that 15% chance I win the money.

Now lets say I get three shots. Get 15 random numbers, number gets drawn out of 100 if I win I win game stops, If i lose we do it again. Get 15 random numbers, number gets drawn out of 100 if I win I win if I lose we do it again. Get 15 random numbers, number gets drawn out of 100 if I win I win if I lose I lose.

So basically I have a 15% chance of winning three times.. what is my overall chances of winning the money?

In: 2

Answer 1

Your odds of winning the first time are .15. Your odds of losing the first time and winning the second time are .85 * .15. Your odds of losing the first and second times but winning the third time are .85 * .85 * .15. Add those up and your odds of winning are about .3858, or 38.58%.