A standard pair of six-sided dice is rolled. What is the probability of rolling a sum less than or equal to 7
? Express your answer as a fraction or a decimal number rounded to four decimal places.
There are a total of 36 possible outcomes when rolling two dice (6 possibilities for the first die and 6 possibilities for the second die).
To find the probability of rolling a sum less than or equal to 7, we need to find the total number of outcomes that result in a sum less than or equal to 7. These are the following combinations:
(1, 1)
(1, 2)
(1, 3)
(1, 4)
(1, 5)
(1, 6)
(2, 1)
(2, 2)
(2, 3)
(2, 4)
(2, 5)
(3, 1)
(3, 2)
(3, 3)
(3, 4)
(4, 1)
(4, 2)
(4, 3)
(5, 1)
(5, 2)
(6, 1)
There are a total of 21 outcomes that result in a sum less than or equal to 7.
Therefore, the probability of rolling a sum less than or equal to 7 is 21/36 or approximately 0.5833 when rounded to four decimal places.