Final answer:
The probability of tossing a head and then rolling a number greater than 3 with a fair coin and a 6-sided die is 1/4, or 25%, as each event has a probability of 1/2, and the product rule is applied to find the combined probability.
Step-by-step explanation:
To find the probability of tossing a head and then rolling a number greater than 3, we consider each event independently and then use the product rule.
The probability of tossing a head with a fair coin is 1/2. To roll a number greater than 3 on a 6-sided die (4, 5, or 6), there are 3 favorable outcomes out of a possible 6, so the probability is 3/6, which simplifies to 1/2. By the product rule, the combined probability of both events happening is:
(Probability of Heads) x (Probability of rolling > 3) = (1/2) x (1/2) = 1/4.
Therefore, the probability of tossing a head and then rolling a number greater than 3 is 1/4, or 25%.