When two dice are rolled,what is the probabil | vedclass

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Question

(C) When two dice are rolled,the total number of outcomes is $n(S) = 6 	imes 6 = 36$.We want the probability that the sum of the numbers is $\leq 10$

Vedclass · Accepted Answer

$\frac{11}{12}$

Vedclass · Answer

(C) When two dice are rolled,the total number of outcomes is $n(S) = 6 	imes 6 = 36$.We want the probability that the sum of the numbers is $\leq 10$.It is easier to calculate the complement: the probability that the sum is $> 10$.The sums greater than $10$ are $11$ and $12$.The outcomes for sum $= 11$ are $(5, 6)$ and $(6, 5)$.The outcome for sum $= 12$ is $(6, 6)$.Thus,the number of outcomes with sum $> 10$ is $n(E') = 3$.The probability of the sum being $> 10$ is $P(E') = \frac{n(E')}{n(S)} = \frac{3}{36} = \frac{1}{12}$.The probability of the sum being $\leq 10$ is $P(E) = 1 - P(E') = 1 - \frac{1}{12} = \frac{11}{12}$.

When two dice are rolled,what is the probability that the sum of the numbers appearing is $\leq 10$?

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