Show that about 45% of the winning pass line bets are made
on the come out roll.
Hint: P( natural | win ) = ?
Let p = P( win ) = 244 / 495
Let natural = The event of rolling 7 or 11
The only way you can win on the come out is to roll a natural.
So, P( win on come out | win ) = P( natural | win )
| P( natural | win ) | = | P( natural and win ) / P( win ) | |
| = | P( natural ) / P( win ) | ||
| = | ( 8 / 36 ) / ( 244 / 495 ) | ||
| = | ( 2 / 9 ) * ( 495 / 244 ) | ||
| = | 55 / 122 ≈ 45.1% | ||
So, given that you won, the probability that you won on the come out is about 45%.