Question

In a simultaneous throw of a pair of dice, find the probability of getting a sum less than 7

Answer 1

We know that in a single throw of two dices, the total number of possible outcomes is (6 × 6) = 36.
Let S be the sample space.
Then n(S) = 36

Let E₁₀ = event of getting a sum less than 7
Then E₁₀ = {(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), (5, 1)}
i.e. n (E₁₀) = 15

\[\therefore P\left( E_{10} \right) = \frac{n\left( E_{10} \right)}{n\left( S \right)} = \frac{15}{36} = \frac{5}{12}\]