Bingo

There's an online bingo game. 90 balls, your card has 15, if all 15 of your numbers are called within 43 picks you win the jackpot. What the odds of that happening? And on average how many picks will it take for your 15 numbers to be called? Just curious, I'm not a math major.

Quote: Jeff571966

There's an online bingo game. 90 balls, your card has 15, if all 15 of your numbers are called within 43 picks you win the jackpot. What the odds of that happening? And on average how many picks will it take for your 15 numbers to be called? Just curious, I'm not a math major.
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Assume that, instead of numbers, there are 15 red balls (yours) and 75 white balls (not yours). You win if the first 43 drawn have all 15 red ones.
Let C(a,b) be "the number of combinations of 'a' things drawn 'b' at a time."
There are C(90,43) sets of 43 balls that can be drawn; if 15 of them are red, then 28 are white, and there are C(75,28) sets of 27 white balls that can be drawn.
The probability of winning = C(75,28) / C(90,43), which is slightly worse than 1 / 300,000.

Average picks is a harder problem, but keep in mind that, since each of the 90 balls has an equal chance of being the last one, there is a 15/90, or 1/6, chance that you will need all 90 balls drawn in order to get all 15 of your numbers called.
I did some simulating, and get an average of about 85.31 balls drawn before all 15 of your numbers are called. This is not surprising when you consider that about 3/5 of the time, at least one of the last five balls will be one of your 15.

Thank you. My roommate took a combinatorics class in college and tried to explain it to me once, didnt get some of it but your explanation makes sense. So 60 percent of the time you won't complete the board until at least 85 balls. That's helpful because that's what everybody is really betting on, getting that complete board first. Thanks for the info.