## Sunday, May 31, 2009

### Puzzle - The three coins

Joe: "I'm going to toss three coins in the air. If they all fall heads, I'll give you \$2. If they all fall talls, I'll give you \$2. But if they fall any other way, you have to give me \$1."

Jim: "Let me think about this a minute. At least two cins will have to be alike because if two don't match, the thrid will have to match one of the other two. And if two are alike, then the thrid coin will match the other two and not match them. The chances are even that the third coin will or won't match. Therefore the chances must be even that Joe is better \$2 against my \$1 that they won't be alike, so the bet should be in my favor. Okay, Joe, I'll take the bet.

Was it waise for Jim to acept the bet?

#### 1 comment:

G said...

i'm not sure how you derived the answer to the 2nd part.

there are 3 coins in the game, each with a 0.5 chance of heads or tails.

For all heads, it is 0.5*0.5*0.5 chance = 1/8

For all tails, it is 0.5*0.5*0.5 chance = 1/8

For any other combination, it is 1 - 1/8 - 1/8 = 6/8

Avg wins per game = (1/8*2)+(1/8*-2)+(6/8*-1) = -0.75

Avg wins for 4 games = -0.75*4=-3