Two dice are rolled together and the product (P) of their scores is obtained :

Event A : P is 6.

Event B : P is an odd number.

Event C : P is 35.

Which of the following event/events has probability equal to 0?

1. Events B and C

2. Events A and B

3. Event B

4. Event C

When two dice are rolled together, possible outcomes are :

{(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}.

No. of possible outcomes = 36

Maximum product of number on dices = 36 when both the dice have 6 on it.

The product one less than the maximum = 30 when one dice have 5 and the other has 6.

∴ No. of favourable outcomes for getting a product of 35 = 0.

∴ P(event C) = $\dfrac{\text{No. of favourable outcomes}}{\text{Total no. of possible outcomes}} = \dfrac{0}{36}$ = 0.

Hence, Option 4 is the correct option.