Probability with Two Fair Dice

Rolling Two Fair Dice

• The probability of rolling a double with two fair dice is 1/6, since there are 6 possible doubles (1,1), (2,2), (3,3), (4,4), (5,5), and (6,6) out of 36 possible outcomes.

Probability of Sum 7

• The probability of rolling a sum of 7 with two fair dice is 6/36, since there are 6 ways to achieve a sum of 7: (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1).

Possible Outcomes

• There are 36 possible outcomes when rolling two fair dice, since each die has 6 possible outcomes (1, 2, 3, 4, 5, and 6) and the two dice can be combined in 6 × 6 = 36 ways.

Probability of Even Numbers

• The probability of rolling an even number on both dice is 9/36, since there are 9 outcomes where both dice show even numbers: (2,2), (2,4), (2,6), (4,2), (4,4), (4,6), (6,2), (6,4), and (6,6).

Probability of Sum Greater Than 10

• The probability of rolling a sum greater than 10 with two fair dice is 3/36, since there are 3 outcomes where the sum is greater than 10: (5,6), (6,5), and (6,6).