In a game of craps, a player loses on the roll if a 2, 3, or 12 is tossed on the first roll. What is the probability of losing on the first roll?

1 Answer

#1/9#

Explanation:

Let's look at the possible rolls we can get with 2 dice rolled, with the 2, 3, and 12 - the losing numbers - coloured in red:

#((color(white)(0),ul1,ul2,ul3,ul4,ul5,ul6),(1|,color(red)2,color(red)3,4,5,6,7),(2|,color(red)3,4,5,6,7,8),(3|,4,5,6,7,8,9),(4|,5,6,7,8,9,10),(5|,6,7,8,9,10,11),(6|,7,8,9,10,11,color(red)12))#

And so out of 36 possibilities, there are 4 that will cause a loss on the first roll.

So that's #P(2,3,12 " on first roll")=4/36=1/9#