Probability

Dear Wizard- My friend and I attend
an event at Casino Pauma in CA on Friday nights. If you are a table player and a
computer picks your name you have an opportunity to spin a wheel for a cash
prize with the Grand prize being $1000. There are approximately 70 table
players at any given time so you have a 1 in 70 chance to be picked. My
friend was called the first night and hit the $1000 prize. There are 40
spots on the wheel and only 1 $1000 prize. The following week my name was
chosen from the table players and I spun the wheel and won the $1000 prize.
We are partners on our wins and was wondering that the odds had to be
incredible for us both to be picked and then spin and win the grand prize.
Could you PLEASE tell us the odds! Please, please, please try and answer
this as it is driving me crazy. Thanks in advance. PS-Thank you soooo much
for your wonderful site!!!

Hi jyager, and welcome to the forums.

If The Wizard doesn't mind, I think I can handle this one =P.

Just break the problem down:

1) The probability of getting your name drawn, P(Drawn) = 1/70 = .0143, (about 1.4%).
2) The probability of getting the top prize on wheel P(TopPrize) = 1/40 = .025 (2.5%)

So what's the odds of just 1 person doing this?

P(drawn & max prize) = P(Drawn) * P(TopPrize) = .0143 * .025 = .00036, or about 1 in 2,750.

So what are the odds you BOTH get picked and BOTH get the top prize?

P(BOTH) = P(drawn & max prize)^2 = .00036^2 = .00000013, or about 1 in 8,000,000.

I'm also just saying what are the odds this happens twice. Not taking in to account "one night after the other" or other random variables the like. Also did some very finite rounding =). Fine hits boys, fine hits =P.

8,000,000 to 1 odds? You're probably misremembering.

/Amidoingitrite?

Alan confirmed that he witnessed it

Thank You sooo much for the answer. Only $2000 and we split it and had to pay taxes. Should have saved that luck for the lottery!!!

Quote: Wizardofnothing

Alan confirmed that he witnessed it

LMAO!!

Quote: Wizardofnothing

Alan confirmed that he witnessed it

Points for you.

Quote: Romes

So what are the odds you BOTH get picked and BOTH get the top prize?

P(BOTH) = P(drawn & max prize)^2 = .00036^2 = .00000013, or about 1 in 8,000,000.

Actually, it's half that, since either one of them could have been picked the first time.

It's 1/35 x 1/40 x 1/70 x 1/40 = 1 in 3,920,000.

Note that this is the probability of both of you hitting the $1000 in the first two nights.

Quote: Wizardofnothing

Alan confirmed that he witnessed it

Well done, sir.