Question:
If A and B are mutually exclusive events such that $p(A)=0.5$ and $p(A\cup B)=0.75$ then $P(B)$ is equal to
If A and B are mutually exclusive events such that $p(A)=0.5$ and $p(A\cup B)=0.75$ then $P(B)$ is equal to
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Logic Tip: "Mutually Exclusive" simply means "no overlap." If event A covers 50% of the possibilities, and A combined with B covers 75%, then B must exactly cover the remaining 25% with no overlapping areas.
Updated On: Apr 30, 2026
- 0.4
- 0.25
- 0.5
- 0.6
- 0.75
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The Correct Option is B
Solution and Explanation
Concept:
The general addition rule for the probability of two events is $P(A \cup B) = P(A) + P(B) - P(A \cap B)$. However, if two events are "mutually exclusive," it means they can never happen at the same time, making the probability of their intersection zero ($P(A \cap B) = 0$).
Step 1: Identify the known probabilities.
From the problem: $$P(A) = 0.5$$ $$P(A \cup B) = 0.75$$
Step 2: Apply the mutually exclusive condition.
Since A and B are mutually exclusive events, their intersection is empty: $$P(A \cap B) = 0$$
Step 3: State the specific addition rule.
The general addition rule simplifies significantly for mutually exclusive events: $$P(A \cup B) = P(A) + P(B)$$
Step 4: Substitute values into the formula.
Plug the known probabilities into the simplified addition rule: $$0.75 = 0.5 + P(B)$$
Step 5: Solve for the unknown probability.
Subtract 0.5 from both sides of the equation to isolate $P(B)$: $$P(B) = 0.75 - 0.50$$ $$P(B) = 0.25$$ Hence the correct answer is (B) 0.25.
The general addition rule for the probability of two events is $P(A \cup B) = P(A) + P(B) - P(A \cap B)$. However, if two events are "mutually exclusive," it means they can never happen at the same time, making the probability of their intersection zero ($P(A \cap B) = 0$).
Step 1: Identify the known probabilities.
From the problem: $$P(A) = 0.5$$ $$P(A \cup B) = 0.75$$
Step 2: Apply the mutually exclusive condition.
Since A and B are mutually exclusive events, their intersection is empty: $$P(A \cap B) = 0$$
Step 3: State the specific addition rule.
The general addition rule simplifies significantly for mutually exclusive events: $$P(A \cup B) = P(A) + P(B)$$
Step 4: Substitute values into the formula.
Plug the known probabilities into the simplified addition rule: $$0.75 = 0.5 + P(B)$$
Step 5: Solve for the unknown probability.
Subtract 0.5 from both sides of the equation to isolate $P(B)$: $$P(B) = 0.75 - 0.50$$ $$P(B) = 0.25$$ Hence the correct answer is (B) 0.25.
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