What Are the Odds of Success in This Promotion

[DSchles]

I'm kind of confused. First you say the "The odds of winning at least once are 100%" Later you say "Therefore, the probability that you'll win at least once is 39.8%." How can it be both 100% and 39.8%. Can you explain? Also I don't understand where the 31/32 numbers come from.

You should have realized that it's impossible for the odds of winning at least once to be 100%. That isn't what I wrote. I wrote: "The odds of winning at least once are 100% - the probability of losing all 16 times." That's a subtraction sign after the 100%! So read it as "minus"!

Also I don't understand where the 31/32 numbers come from.

That's the probability of picking five games and NOT winning all of them. You have a 1/2 chance to win one game. So you have a (1/2)^5 = 1/32 of winning all five games. Therefore, you have a 1 - 1/32 = 31/32 of NOT winning all five games. Not winning all five games 16 times in a row, as stated above, would then be (31/32)^16 = 60.2%, which means you have a 1 - .602 = .398 = 39.8% chance of winning all five at least once in 16 weeks. Of course, if you think you have any handicapping ability (don't we all!), you might increase the odds a little bit.

Finally, you know the drill with variance. MAYBE you'll win once. Maybe not at all. Maybe twice. REALLY lucky--three times.

Don

[21forme]

(don't we all!)

No.

[DSchles]

No.

Very big club! Actually the club of those who THINK they have handicapping ability is considerably larger than those who actually do. Not sure if the club of those who already know they don't is larger or smaller than the former group.

Don