The Question
A and B are mutually exclusive events. If P(A) = 0,42 and P(A or B) = 0,79, calculate P(B).
Details
💡 Hint
What does ‘mutually exclusive’ tell you about the relationship between P(A or B), P(A), and P(B)? There’s a very straightforward formula for this!
📝 Solution Steps
- 1. Recall the formula for the probability of mutually exclusive events.
- 2. Substitute the given values for P(A) and P(A or B) into the formula.
- 3. Solve the resulting equation for P(B).
📚 Explanation
For mutually exclusive events, the probability of either event A or event B occurring is simply the sum of their individual probabilities. This is because they cannot happen at the same time, so there’s no overlap to subtract. The formula is P(A or B) = P(A) + P(B). You are given P(A) and P(A or B), so you can substitute these values into the formula and solve for P(B).
✅ Answer
0.37
⚠️ Common Mistakes
- Using the general addition rule P(A or B) = P(A) + P(B) – P(A and B) without realizing that P(A and B) = 0 for mutually exclusive events.
- Simple arithmetic errors during calculation.
📐 Formulas Required
- P(A or B) = P(A) + P(B) (for mutually exclusive events)