# If two dice are rolled simultaneously, find the probability of the following events. Event A: The sum of the digits on the upper faces is at least 10 - Algebra

Sum

If two dice are rolled simultaneously, find the probability of the following events.

Event A: The sum of the digits on the upper faces is at least 10

#### Solution

Sample space,

S = {(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)}

∴ n(S) = 36

Let A be the event that the sum of the digits on the upper faces is at least 10.

∴ A = {(4, 6), (5, 5), (5, 6), (6, 4), (6, 5), (6, 6)}

∴ n(A) = 6

∴ P(A) = ("n"("A"))/("n"("S"))

= 6/36

∴ P(A) = 1/6

Concept: Probability of an Event
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