A standard pair of six-sided dice is rolled. What is the probability of rolling a sum less than 10? Express your answer as a fraction or a decimal number rounded to four decimal places.
To find the total number of possible outcomes when rolling two six-sided dice, we calculate: 6 possibilities for the first die, and 6 possibilities for the second die, resulting in a total of 6 x 6 = 36 possible outcomes.
To find the total number of outcomes where the sum is less than 10, we find the pairs that satisfy this condition:
(1,1), (1,2), (1,3), (1,4), (1,5), (1,6)
(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)
(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)
(4,1), (4,2), (4,3), (4,4), (4,5)
(5,1), (5,2), (5,3), (5,4)
(6,1), (6,2), (6,3)
There are 28 possible outcomes where the sum is less than 10.
Therefore, the probability of rolling a sum less than 10 is 28/36 = 7/9 ≈ 0.7778.
Rounded to four decimal places, the probability is 0.7778.