Question

Two fair dice are thrown. The probability that the product is divisible by 3 is
a) 4/9
b) 5/9
c) 2/3
d) 7/9​

Answer 1

b) 5/9, please read the answer below.

Let's first see which events follow the given condition. It is required at least one die is 3 or 6, to be divisible by 3.

The events of the first die

3×1, 3×2, ..., 3×6(6 events)

6×1, 6×2, ..., 6×6(6 events)

The events of the second die

1×3, 2×3, ..., 6×3(6 events)

1×6, 2×6, ..., 6×6(6 events)

3×3 and 6×6 happen in both events. So 2 events should be forgotten.

There are a total of 6×6 events. 20 events satisfy the given conditions. So, the probability is 20/36=5/9.