In a single throw with two dice, find the probability that their sum is a…

Solution:

We need the probability that the sum of two dice is a multiple of 3 or 4.

Multiples of 3 or 4 between 2 and 12 are: 3, 4, 6, 8, 9, 12.

• Sum 3: 2 ways (1+2, 2+1)

• Sum 4: 3 ways (1+3, 2+2, 3+1)

• Sum 6: 5 ways (1+5, 2+4, 3+3, 4+2, 5+1)

• Sum 8: 5 ways (2+6, 3+5, 4+4, 5+3, 6+2)

• Sum 9: 4 ways (3+6, 4+5, 5+4, 6+3)

• Sum 12: 1 way (6+6)

Total favorable outcomes = 2 + 3 + 5 + 5 + 4 + 1 = 20.

Total possible outcomes = 6 × 6 = 36. Therefore probability = 20/36 = 5/9.