Hello, prasum!

A man throws a die three times.

If in first throw, an odd prime number occurs

. . he adds the numbers appearing in the next two throws.

Otherwise, he multiplies them.

Find the probability that the number thus obtained is even number.

The first throw is a prime: {3, 5}. .

The sum of the next two throws is even.

. . . .

. . . .

So:

Hence:

The first throw is not a prime: {1, 2, 4, 6}. .

The product of the next two throws is odd.

. .

So:

Hence:

Therefore: