Final answer:
The values that can represent the probability of an event include 0, 1, and 1/2, with -0.5 being invalid as it is negative. In provided example scenarios, probabilities were computed for mutually exclusive and independent events.
Step-by-step explanation:
The probabilities that can represent an event are A. 0, B. 1, and C. 1/2. These values are valid because probabilities can range from 0 to 1, inclusive. This is because a probability of 0 indicates the event cannot occur, a probability of 1 means the event is certain to occur, and any fraction between 0 and 1 indicates the likelihood of the event's occurrence.
The correct probabilities related to the questions provided are:
- For mutually exclusive events H and D with P(H) = .25 and P(D) = .15, the probability P(HD) is B. 0, because mutually exclusive events cannot occur simultaneously.
- For independent events A and B with P(A) = .2 and P(B) = .3, the probability P(A AND B) is D. .06, which is calculated by multiplying the probabilities of A and B (P(A) × P(B)).
Thus, in these contexts, -0.5 (D. -0.5) cannot be a probability because probabilities cannot be negative. Probabilities are always non-negative numbers.