Two unbiased dice are thrown once. Write all | vedclass

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Question

(A) When two unbiased dice are thrown,the total number of possible outcomes is $6 	imes 6 = 36$. The sample space $S$ is given by:$S = \{(1,1), (1,2)

Vedclass · Accepted Answer

$\frac{1}{36}$

Vedclass · Answer

(A) When two unbiased dice are thrown,the total number of possible outcomes is $6 	imes 6 = 36$. The sample space $S$ is given by:$S = \{(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)\}$We need the sum of the numbers on the two dice to be a multiple of both $3$ and $4$. The least common multiple of $3$ and $4$ is $12$. Thus,we are looking for outcomes where the sum is $12$.The only outcome where the sum is $12$ is $(6,6)$.Number of favorable outcomes $= 1$.Probability $P(E) = \frac{	ext{Number of favorable outcomes}}{	ext{Total number of outcomes}} = \frac{1}{36}$.

Two unbiased dice are thrown once. Write all the possible outcomes of this experiment. What is the probability that the sum of the numbers on the two dice is a multiple of $3$ and $4$?

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