Assuming a standard six-sided die and a fair coin, the probability of rolling a composite number (any number that is not a prime number) on the die is 3/6 or 1/2, since there are three composite numbers (4, 6, 8) out of six possible outcomes (1, 2, 3, 4, 5, 6).
The probability of the coin landing on heads is 1/2, and the probability of it landing on tails is also 1/2. Therefore, the probability of both events happening together is:
P(composite number and heads and tails) = P(composite number) x P(heads) x P(tails)
P(composite number and heads and tails) = (1/2) x (1/2) x (1/2)
P(composite number and heads and tails) = 1/8
So the probability of rolling a composite number and the coin landing on heads and tails is 1/8.