Events \( A \) and \( B \) are mutually exclusive. Suppose event \( A \) occurs with probability, 0.43 and event \( B \) occurs with probability 0.18 . Compute the following. (If necessary, consult a list of formulas.) (a) Compute the probability that \( B \) occurs but \( A \) does not occur. (b) Compute the probability that either \( B \) occurs without \( A \) occurring or \( A \) and \( B \) both occur. \( \square \)

To solve these probability problems, let's start by analyzing the given probabilities: 1. The probability of event \( A \) occurring is \( P(A) = 0.43 \). 2. The probability of event \( B \) occurring is \( P(B) = 0.18 \). 3. Since events \( A \) and \( B \) are mutually exclusive, they cannot happen at the same time. Now, let's compute the required probabilities. (a) To compute the probability that \( B \) occurs but \( A \) does not, we can use the formula: \[ P(B \text{ and not } A) = P(B) - P(A \text{ and } B) \] Since \( A \) and \( B\) are mutually exclusive, \( P(A \text{ and } B) = 0\). Thus, \[ P(B \text{ and not } A) = P(B) = 0.18 \] (b) Next, we need to compute the probability that either \( B \) occurs without \( A \) occurring or both \( A \) and \( B \) occur. Since we already established that \( A \) and \( B \) cannot occur together, \[ P(B \text{ and not } A) \text{ or } P(A \text{ and } B) = P(B \text{ and not } A) + P(A \text{ and } B) \] Substituting the values we found: \[ P(B \text{ and not } A) = 0.18 \] \[ P(A \text{ and } B) = 0 \] Thus, \[ P(B \text{ and not } A \text{ or } A \text{ and } B) = 0.18 + 0 = 0.18 \] So the answers are: (a) \( P(B \text{ and not } A) = 0.18 \) (b) \( P(B \text{ and not } A \text{ or } A \text{ and } B) = 0.18 \)