Two dice are thrown together. If the numbers | vedclass

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Question

(C) When two dice are thrown,the total number of outcomes is $6 	imes 6 = 36$. The outcomes where the numbers on the two dice are the same are $(1,1)

Vedclass · Accepted Answer

$\frac{2}{15}$

Vedclass · Answer

(C) When two dice are thrown,the total number of outcomes is $6 	imes 6 = 36$. The outcomes where the numbers on the two dice are the same are $(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)$,which are $6$ outcomes. The number of outcomes where the numbers are different is $36 - 6 = 30$. The outcomes where the sum is $6$ are $(1,5), (2,4), (3,3), (4,2), (5,1)$. Since we are given that the numbers must be different,we exclude $(3,3)$. The favorable outcomes are $(1,5), (2,4), (4,2), (5,1)$,which are $4$ outcomes. The required probability is $\frac{4}{30} = \frac{2}{15}$.

Two dice are thrown together. If the numbers appearing on the two dice are different,then what is the probability that the sum is $6$?

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