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(A) When two dice are thrown, the total number of possible outcomes is $6 	imes 6 = 36$. On a single die, the prime numbers are $\{2, 3, 5\}$ and the

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$\frac{1}{3}$

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(A) When two dice are thrown, the total number of possible outcomes is $6 	imes 6 = 36$. On a single die, the prime numbers are $\{2, 3, 5\}$ and the composite numbers are $\{4, 6\}$. Note that $1$ is neither prime nor composite. We need the probability of getting a prime number on one die and a composite number on the other. The possible outcomes are: $(2, 4), (2, 6), (3, 4), (3, 6), (5, 4), (5, 6)$ (prime on first, composite on second) $(4, 2), (6, 2), (4, 3), (6, 3), (4, 5), (6, 5)$ (composite on first, prime on second) Total favorable outcomes = $6 + 6 = 12$. Probability = $\frac{	ext{Favorable outcomes}}{	ext{Total outcomes}} = \frac{12}{36} = \frac{1}{3}$.

When two dice are thrown, the probability of getting a prime number on one die and a composite number on the other is

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