Answer :
Final answer:
The probabilities of Events A, B, and C are found by adding the individual probabilities of their outcomes. The probabilities of Events F, G, and H can be determined from the probabilities of Events A, B, and C since the latter events contain the outcomes of the former. Thus, option D is correct.
Explanation:
To calculate the probabilities of partitioned events, we must understand that all outcomes in a sample space are equally likely, and the sum of probabilities for all disjoint events must equal 1. For instance, if we know the probabilities of Events A, B, and C, we can use them to find the probabilities of Events F, G, and H in Partitioning III.
For Events A, B, and C:
- Event A = a or b or c
- Event B = d
- Event C = e or f
The probability of Event A, B, or C is the sum of the individual probabilities of outcomes a, b, c for A; d for B; e, f for C, respectively.
For Event F, G, and H:
- Event F = a or b (contained within Event A)
- Event G = c or d (c is part of Event A and d is Event B)
- Event H = e or f (Event C)
The probabilities of Events F, G, and H can indeed be expressed in terms of the probabilities of Events A, B, and C since each outcome in F, G, H is included in one of these previous partitions. For example, the probability of Event F is the sum of the probabilities of outcomes a and b, which are part of Event A. Thus, option D is correct.
