Questions: Please find P(A does not occur)

Solution Steps

The total probability of all events in the sample space must sum to 1. The given probabilities are:

• P(A ∩ B) = 0.2
• P(A only) = 0.15
• P(B only) = 0.4
• P(neither A nor B) = 0.25

The probability of A occurring is the sum of the probabilities of A only and A ∩ B: \[ P(A) = P(A \text{ only}) + P(A \cap B) \] \[ P(A) = 0.15 + 0.2 = 0.35 \]

The probability of A not occurring is the complement of the probability of A occurring: \[ P(A^c) = 1 - P(A) \] \[ P(A^c) = 1 - 0.35 = 0.65 \]

Final Answer