Franklin rolls a pair of six-sided fair dice with sides numbered 1 through 6.the probability that the sum of the numbers rolled is either a multiple of 3 or 4 is

The probability that the sum of the numbers rolled is either a multiple of 3 or 4 is 5/9.

Step-by-step explanation:

As given:  Franklin rolls a pair of six-sided fair dice with sides numbered 1 through 6.

A pair of dice has 36  possible outcomes.

The probability that the sum of the numbers rolled is either a multiple of 3 or 4 is or

Let 'A' and 'B' be the events that the sum of the numbers rolled is a multiple of 3 and a multiple of 4 respectively.

Set for A = {(1, 2), (1, 5), (2, 1), (2, 4), (3, 3), (3, 6), (4, 2), (4, 5), (5, 1), (5, 4), (6, 3), (6, 6)},  and set for B = {(1, 3), (2, 2), (2, 6), (3, 1), (3, 5), (4, 4), (5, 3), (6, 2), (6, 6)}.

So, together they form 20 sets ((6,6) is repeating so take once)

Hence, we get 20/36=5/9