I'm stumped by a probability issue I'm trying to work out whilst coding. My math isn't up to the task! In simplest terms it could be worked out to this fictional scenario:
Jack bought raffle tickets for three different draws. Due to the total number of tickets sold for each draw he knows that:
He has a 1/4 chance of winning Game 1
He has a 1/8 chance of winning Game 2
He has a 1/16 chance of winning Game 3
What is his overall chance of winning something (at least one draw)?
When I did 1/2 chance for each draw and played with some numbers, I figured out through trial and error it was around 87.5%, but I can't arrive at the number elegantly, and I certainly haven't figured it out when each draw has a different chance. Help!