Three dice are thrown at the same time. Find the probability of gettin

1.	Three dice are thrown at the same time. Find the probability of getting three two’s, if it is known that the sum of the numbers on the dice was six.
Answer» Given that the dice is thrown three times So, the sample space n(S) = 6³ = 216 Let E₁ be the event when the sum of number on the dice was 6 and E₂ be the event when three 2’s occur. E₁ = {(1, 1, 4), (1, 2, 3), (1, 4, 1), (2, 1, 3), (2, 2, 2), (2, 3, 1), (3, 1, 2), (3, 2, 1), (4, 1, 1)} n(E₁) =10 and n(E₂) = 1 [Since, E₂ = (2, 2, 2)] Thus, P(E₂/E₁) = P(E₁⋂ E₂)/P(E₁) = (1/216)/(10/216) = 1/10.

Three dice are thrown at the same time. Find the probability of getting three two’s, if it is known that the sum of the numbers on the dice was six.

Answer»

Given that the dice is thrown three times

So, the sample space n(S) = 6³ = 216

Let E₁ be the event when the sum of number on the dice was 6 and E₂ be the event when three 2’s occur.

E₁ = {(1, 1, 4), (1, 2, 3), (1, 4, 1), (2, 1, 3), (2, 2, 2), (2, 3, 1), (3, 1, 2), (3, 2, 1), (4, 1, 1)}

n(E₁) =10 and n(E₂) = 1 [Since, E₂ = (2, 2, 2)]

Thus, P(E₂/E₁) = P(E₁⋂ E₂)/P(E₁) = (1/216)/(10/216) = 1/10.

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Three dice are thrown at the same time. Find the probability of getting three two’s, if it is known that the sum of the numbers on the dice was six.

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