Two unbiased dice are thrown once. Write all | vedclass

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(D) The sample space $S$ for throwing two unbiased dice is given by the set of all possible ordered pairs $(x, y)$ where $x, y \in \{1, 2, 3, 4, 5, 6\

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(D) The sample space $S$ for throwing two unbiased dice is given by the set of all possible ordered pairs $(x, y)$ where $x, y \in \{1, 2, 3, 4, 5, 6\}$.There are $6 	imes 6 = 36$ possible outcomes:$S = \{(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)\}$Let $E$ be the event that the sum of the numbers on the two dice is smaller than $13$.The minimum sum is $1 + 1 = 2$ and the maximum sum is $6 + 6 = 12$.Since the maximum possible sum is $12$,which is always less than $13$,every outcome in the sample space satisfies the condition.Thus,$E = S$ and the number of favorable outcomes is $36$.The probability $P(E) = \frac{	ext{Number of favorable outcomes}}{	ext{Total number of outcomes}} = \frac{36}{36} = 1$.Therefore,the probability is $1$.

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 smaller than $13$?

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