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Question
Two different dice are rolled simultaneously. Find the probability that the sum of the numbers on the two dice is 10.
Solution
When two different dice are thrown, then total number of outcomes = 36.
Let E be the event of getting the sum of the numbers less than 7.
These numbers are (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (2, 1), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (3, 3), (4, 1), (4, 2) and (5, 1).
Number of Favourable outcomes = 15
∴ P(getting the sum of the numbers on the two dice is 10) `= P(E_) = "NUmber of outcomes favourable"/"(Number of all possible outcomes)"`
`= 15/36 = 5/12`
thus, the probability of getting the sum of the numbers less than 7 is`5/12`
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