Three heads up

[kentmclean at mindspring.com (Kent McLean)]

Chris wrote:
>
Heads Up
>  The possible combinations for heads up are:        0
>
1
>
2
>
3
>
> Why wouldn't the answer be one in 4?

Because with 1 Heads up, it could be the a) first coin,
or b) the second coin, or c) the third coin.  For two
heads, it could be d) the first and second, e) the first
and third, or f) the second and third.  So you have to
add b), c), e), and f) into your picture, going from
4 solutions to 8.

Look at it this way:

Toss 1:    H-H-H
Toss 2:    H-H-T
Toss 3:    H-T-H
Toss 4:    H-T-T
Toss 5:    T-T-T
Toss 6:    T-T-H
Toss 7:    T-H-T
Toss 8:    T-H-H

All Heads turns up only in Toss 1, out of 8 possible results.
So, it's 1 chance in 8. Or 1/2*1/2*1/2, or 1/(2^3).

Comprenez-vous?

Kent