Question 36

Explanation

To solve this probability problem, first determine the sample space and the required events.

Determining the Sample Space

When two dice are thrown together, the total possible outcomes are

Event A with Sum of Dice Equal to 5

The pairs of dice with sum 5 are $(1,4)$, $(4,1)$, $(2,3)$, $(3,2)$

The number of outcomes in event A is $n(A) = 4$

Probability of event A

Event B with Sum of Dice Equal to 7

The pairs of dice with sum 7 are $(2,5)$, $(5,2)$, $(4,3)$, $(3,4)$, $(6,1)$, $(1,6)$

The number of outcomes in event B is $n(B) = 6$

Probability of event B

Calculating the Combined Probability

Since events A and B are mutually exclusive (cannot occur simultaneously), then

Therefore, the probability that the sum of the dice is 5 or 7 is $\frac{10}{36}$