Two unbiased dice are thrown once. Write all | vedclass

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(A) When two unbiased dice are thrown,the sample space $S$ consists of all possible ordered pairs $(x, y)$ where $x, y \in \{1, 2, 3, 4, 5, 6\}$.The t

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$\frac{1}{12}$

Vedclass · Answer

(A) When two unbiased dice are thrown,the sample space $S$ consists of all possible ordered pairs $(x, y)$ where $x, y \in \{1, 2, 3, 4, 5, 6\}$.The total number of elementary outcomes is $6 	imes 6 = 36$.The sample space is:$S = \{(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)\}$Let $B$ be the event that the sum of the numbers on the two dice is $4$.The outcomes favourable to event $B$ are $(1,3), (2,2), (3,1)$.The number of favourable outcomes is $n(B) = 3$.The probability of event $B$ is given by $P(B) = \frac{n(B)}{n(S)} = \frac{3}{36} = \frac{1}{12}$.

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

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