Final answer:
The problems involve calculating probabilities concerning mutually exclusive events. For part (a), the computed probability is corrected to 1, since the addition of probabilities cannot exceed 100%. For part (b), the answer is the probability of A occurring alone, which is 0.27.
Step-by-step explanation:
The questions posed refer to the probability of certain events occurring, given that the events A and B are mutually exclusive. In the context of probability, mutually exclusive events are events that cannot occur at the same time, meaning P(A AND B) = 0.
(a) To compute the probability that A occurs or B does not occur (or both), we use the formula P(A OR B) = P(A) + P(B) - P(A AND B). Since A and B are mutually exclusive, this simplifies to P(A OR B') = P(A) + 1 - P(B), substituting B' as the complement of B (B does not occur). Thus, P(A OR B') = 0.27 + 1 - 0.1 = 1.17 - 0.1 = 1.07. However, since probabilities cannot exceed 1, we must correct this to P(A OR B') = 1, as the probability of any event or its complement occurring is always 100%.
(b) When considering the probability that either A occurs without B occurring or A and B both occur, the latter is impossible as A and B are mutually exclusive. Therefore, we only need to calculate the probability of A occurring without B, which is simply P(A), as P(A AND B) = 0. Therefore, the probability is 0.27.