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

Vedclass · Accepted Answer

$1/6, 5/18$

Vedclass · Answer

(A) When two dice are thrown,the sample space is $S = \{(1, 1), (1, 2), ..., (6, 6)\}$.The total number of outcomes is $n(S) = 6 	imes 6 = 36$.$(1)$ Let $E_1$ be the event that the numbers on both dice are the same.$E_1 = \{(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)\}$.$n(E_1) = 6$.$P(E_1) = \frac{n(E_1)}{n(S)} = \frac{6}{36} = \frac{1}{6}$.$(2)$ Let $E_2$ be the event that the difference between the numbers is $1$.$E_2 = \{(1, 2), (2, 1), (2, 3), (3, 2), (3, 4), (4, 3), (4, 5), (5, 4), (5, 6), (6, 5)\}$.$n(E_2) = 10$.$P(E_2) = \frac{n(E_2)}{n(S)} = \frac{10}{36} = \frac{5}{18}$.

When two dice are thrown simultaneously,find the probability of the following:
$(1)$ The numbers are the same.
$(2)$ The difference between the numbers is $1$.

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When two dice are thrown simultaneously,find the probability of the following:$(1)$ The numbers are the same.$(2)$ The difference between the numbers is $1$.