A die is rolled & a coin is tossed. Find probability that the die shows an odd…

Concept: When two experiments are independent (the outcome of one does not affect the other), the probability that both of two events occur together equals the product of their individual probabilities: P(A and B) = P(A) x P(B).

1. A fair die has 6 equally likely faces {1, 2, 3, 4, 5, 6}. The odd faces are 1, 3, 5, so P(die shows odd) = 3/6 = 1/2.

2. A fair coin has 2 equally likely faces {H, T}, so P(coin shows head) = 1/2.

3. Rolling the die and tossing the coin are independent experiments, so P(die shows odd and coin shows head) = 1/2 x 1/2 = 1/4.

Cross-check: List the combined sample space directly - 6 die faces x 2 coin faces = 12 equally likely outcomes. Only 3 of them pair an odd face with a head: (1, H), (3, H), (5, H). This gives 3/12 = 1/4, confirming the result obtained above.