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

You need to look at the “complement”. The only way to *not* win is to lose all three times. There’s an 85% chance of losing on each attempt. 1-0.85^(3) ≈ 0.39 = 39% chance of winning.