When two dice are thrown simultaneously,what | vedclass

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(B) When two dice are thrown,the total number of possible outcomes is $n(S) = 6 	imes 6 = 36$.The sum of the numbers on the two dice can range from $

Vedclass · Accepted Answer

$1/2$

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(B) When two dice are thrown,the total number of possible outcomes is $n(S) = 6 	imes 6 = 36$.The sum of the numbers on the two dice can range from $2$ to $12$.For the sum to be an odd number,it must be $3, 5, 7, 9,$ or $11$.Let us list the favorable outcomes for each sum:- Sum $= 3$: $(1, 2), (2, 1)$ ($2$ outcomes)- Sum $= 5$: $(1, 4), (4, 1), (2, 3), (3, 2)$ ($4$ outcomes)- Sum $= 7$: $(1, 6), (6, 1), (2, 5), (5, 2), (3, 4), (4, 3)$ ($6$ outcomes)- Sum $= 9$: $(3, 6), (6, 3), (4, 5), (5, 4)$ ($4$ outcomes)- Sum $= 11$: $(5, 6), (6, 5)$ ($2$ outcomes)Total number of favorable outcomes $n(E) = 2 + 4 + 6 + 4 + 2 = 18$.The probability $P(E) = \frac{n(E)}{n(S)} = \frac{18}{36} = \frac{1}{2}$.

When two dice are thrown simultaneously,what is the probability that the sum of numbers appeared is an odd number?

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