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Probability: jackpots

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!

cyberkiwi

You need to draw a Venn diagram to see this, there will be 7 sections.
The ONLY section that doesn't win anything is
doesn't win game1 AND doesn't win game2 AND doesn't win game3
This is easily calculated as
3/4 * 7/8 * 15/16

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cyberkiwi

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HainKurt

He has a 1/4 chance of winning Game 1 = 3/4 losing
He has a 1/8 chance of winning Game 2 = 7/8 loosing
He has a 1/16 chance of winning Game 3 = 15/16 loosing

(3/4)*(7/8)*(15/16) = 0.6152

so he will not get anything %61.52 and get 1- 0.6152 = 0.3847, %39.47 somehing...

tknudsen-qec

ASKER

Thank you so very much, this is extremely helpful and appreciated.

babesia

As cyberkiwi said.

P(win something) = 1 - (1 - 1/4) x (1- 1/8) x (1 - 1/16) = 1 - 0.615234375 = 0.38476525