What's the probability of getting craps or an even sum on a single dice roll?

Hi @xah!

To calculate the probability of getting craps or an even sum on a single roll of a standard six-sided die, we need to break it down into two parts:

1. Craps: In craps, rolling a 2, 3, or 12 on the first roll is considered "craps," and the player loses their bet. 

There is one way to roll a 2 (1+1), two ways to roll a 3 (1+2 or 2+1), and one way to roll a 12 (6+6). 

So, there are a total of 4 ways to roll craps.

There are two dice, each with six sides, so there are a total of 6 * 6 = 36 possible outcomes when rolling two dice.

• Probability of rolling craps = (Number of Favorable Outcomes) / (Total Number of Possible Outcomes) = 4 / 36 = 1/9.
• Probability as a percentage = (1/9) * 100 = 11.11%

2. Even Sum: An even sum can occur when rolling a 2, 4, 6, 8, 10 and 12. 

Check the breakdown below for each number:

• There is one way to roll a 2 (1+1);
• Three ways to roll a 4 (1+3, 2+2, or 3+1);
• Three ways to roll a 4 (1+3, 2+2, or 3+1);
• Five way to roll a 6 (3+3);
• Five ways to roll an 8;
• Two ways to roll a 10;
• One way to roll a 12.

So, there are a total of 17 ways to roll an even sum.

Now, calculate the probability:

• Probability of getting an even sum = (Number of Even Sum Outcomes) / (Total Number of Possible Outcomes) = 17 / 36
• Probability as a percentage = (17/36) * 100 = 47.22%
  
  Hope you find this helpful!