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