Two balanced dice are rolled. Find the probab | vedclass

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Question

(A) When two dice are rolled,the total number of possible outcomes is $6 	imes 6 = 36$.Let the outcomes be $(x, y)$ where $x$ and $y$ are the numbers

Vedclass · Accepted Answer

$\frac{1}{2}$

Vedclass · Answer

(A) When two dice are rolled,the total number of possible outcomes is $6 	imes 6 = 36$.Let the outcomes be $(x, y)$ where $x$ and $y$ are the numbers on the first and second die respectively.The sum $(x + y)$ is even if:$1.$ Both $x$ and $y$ are odd: There are $3$ choices for $x$ $(1, 3, 5)$ and $3$ choices for $y$ $(1, 3, 5)$. Total outcomes = $3 	imes 3 = 9$.$2.$ Both $x$ and $y$ are even: There are $3$ choices for $x$ $(2, 4, 6)$ and $3$ choices for $y$ $(2, 4, 6)$. Total outcomes = $3 	imes 3 = 9$.Total favorable outcomes = $9 + 9 = 18$.Probability = $\frac{	ext{Favorable outcomes}}{	ext{Total outcomes}} = \frac{18}{36} = \frac{1}{2}$.

Two balanced dice are rolled. Find the probability that the sum of numbers on two dice is even.

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