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Question
Two dice are rolled together. Find the probability of getting a total of at least 10.
Solution
n(S) = 36 i.e.
(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),(4, 6)
(5, 1),(5, 2),(5, 3),(5, 4),(5, 5),(5, 6)
(6, 1),(6, 2),(6, 3),(6, 4),(6, 5),(6, 6)
In throwing a dice, total possible outcomes = {1, 2, 3, 4, 5, 6}
n(S) = 6
For two dice, n(S) = 6 × 6 = 36
E = event of getting a total of at least 10 = {(4, 6),(5, 5),(5, 6),(6, 4),(6, 5),(6, 6)}
n(E) = 6
Probability of getting a total of at least 10 = `(n(E))/(n(S)) = 6/36 = 1/6`
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