math/probability gurus

[snoozer]

So, we have a group pool for the mega millions at work. For the draw on Tuesday, we had 90 tickets and won 0 dollars.

What is the probability of not having a winning ticket with 90 picks
Here are the rules and how to win
Players may pick six numbers from two separate pools of numbers - five different numbers from 1 to 56 and one number from 1 to 46 - or select Easy Pick. You win the jackpot by matching all six winning numbers in a drawing.
Match
5 in P1 and 1 in P2 - odds 1 in 175,711,536
5 in P1 and 0 in P2 - odds 1 in 3,904,701
4 in P1 and 1 in P2 - odds 1 in 689,065
4 in P1 and 0 in P2 - odds 1 in 15313
3 in P1 and 1 in P2 - odds 1 in 13781
3 in P1 and 0 in P2 - odds 1 in 306
2 in P1 and 1 in P2 - odds 1 in 844
1 in P1 and 1 in P2 - odds 1 in 141
0 in P1 and 1 in P2 - odds 1 in 75
Overall odds of winning 1-40

 

[marine]

So, we have a group pool for the mega millions at work. For the draw on Tuesday, we had 90 tickets and won 0 dollars.

What is the probability of not having a winning ticket with 90 picks
Here are the rules and how to win
Players may pick six numbers from two separate pools of numbers - five different numbers from 1 to 56 and one number from 1 to 46 - or select Easy Pick. You win the jackpot by matching all six winning numbers in a drawing.
Match
5 in P1 and 1 in P2 - odds 1 in 175,711,536
5 in P1 and 0 in P2 - odds 1 in 3,904,701
4 in P1 and 1 in P2 - odds 1 in 689,065
4 in P1 and 0 in P2 - odds 1 in 15313
3 in P1 and 1 in P2 - odds 1 in 13781
3 in P1 and 0 in P2 - odds 1 in 306
2 in P1 and 1 in P2 - odds 1 in 844
1 in P1 and 1 in P2 - odds 1 in 141
0 in P1 and 1 in P2 - odds 1 in 75
Overall odds of winning 1-40

50/50.
either you win or you dont.

 

[Mags]

Here's my take:

Your odds of winning ANYTHING for a given ticket is 1/41 (odds are 1 of 40)...

So your odds of NOT winning with a given ticket is 40/41 = 97.5%

I'm assuming that the numbers of the 90 tickets are all different (no 2 tickets are identical), so

Your odds of NOT winning anything with 90 tickets would be 97.5%, raised to the 90th power, or 0.108.

Which means your odds of having 1 or more winning tickets is 1-0.108 = .892.

Or in other words, you had a 89.2% chance of having at least one winning ticket.

Or, in other words, you got screwed.

 

[slim pickins]

If I recall my high school math correctly and looking at your odds payoff chart I think it goes like this:

At the bottom of your payoff chart the overall odds of winning are 1 in 40. So the chances of not winning are 39 in 40.

39/40=0.975

If you bought 2 tickets, chances of not winning are:
(0.975)*(0.975)=0.951

If you bought 3 tickets, chances of not winning are:
(0.975)*(0.975)*(0.975)=0.927

If you bought 4 tickets, chances of not winning are:
(0.975)*(0.975)*(0.975)*(0.975)=0.904

and on and on...

So with 90 tickets you get:
0.975^90 (raised to the exponent of 90 tickets)

which equals 0.102


This is roughly a 10% chance (1 in 10).
I'd say you got a rough break.

You would have a fifty-fifty chance of winning with 27 tickets. (50.5%)

 

[slim pickins]

Damn you Mags!

You beat me by 2 mintues!

What are the chances of that?

 

[Mags]

Damn you Mags!

You beat me by 2 mintues!

What are the chances of that?

Early bird gets the worm....

It was nice to get confirmation on my answer (although you had a different interpretation of the 1-40 - it could be your's or mine).....

Even though I'm an actuary, I haven't used probability skills in a long time - so it is nice to get confirmation!

 

[slim pickins]

You would have a fifty-fifty chance of winning with 27 tickets. (50.5%)

That's a 50.5% of not winning. So it should read 49.5% chance of winning.

(Stay away from lotteries... sports betting gets you more bang for your buck. Remember to tip your waitress, but for the love of God if your married DON"T date them. Sermon over... Amen)