Español Events A and B are mutually exclusive. Suppose event A occurs with probability 0.4 and event B occurs with probability 0.35. Compute the following. (If necessary, consult a list of formulas.) (a) Compute the probability that B occurs but A does not occur. 0 Compute the probability that (b) either A occurs without B occurring or A and B both occur.

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**Mutually Exclusive Events: Probability Calculation**

**Problem Statement:**

Two events, \( A \) and \( B \), are mutually exclusive. Let the probability of event \( A \) be 0.4 and the probability of event \( B \) be 0.35.

**Tasks:**

(a) Calculate the probability that event \( B \) occurs but event \( A \) does not occur.

(b) Calculate the probability that either event \( A \) occurs without \( B \) occurring, or both events \( A \) and \( B \) occur.

**Steps:**

1. Review the concept of mutually exclusive events. Mutually exclusive means that both events cannot occur at the same time.

2. For task (a), since \( A \) and \( B \) are mutually exclusive, \( B \) occurring implies \( A \) does not occur.

3. For task (b), determine the scenarios: event \( A \) occurring while \( B \) does not, or checking if both events occurring can be possible despite the mutual exclusivity statement.
Transcribed Image Text:**Mutually Exclusive Events: Probability Calculation** **Problem Statement:** Two events, \( A \) and \( B \), are mutually exclusive. Let the probability of event \( A \) be 0.4 and the probability of event \( B \) be 0.35. **Tasks:** (a) Calculate the probability that event \( B \) occurs but event \( A \) does not occur. (b) Calculate the probability that either event \( A \) occurs without \( B \) occurring, or both events \( A \) and \( B \) occur. **Steps:** 1. Review the concept of mutually exclusive events. Mutually exclusive means that both events cannot occur at the same time. 2. For task (a), since \( A \) and \( B \) are mutually exclusive, \( B \) occurring implies \( A \) does not occur. 3. For task (b), determine the scenarios: event \( A \) occurring while \( B \) does not, or checking if both events occurring can be possible despite the mutual exclusivity statement.
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