Practice Questions
Concept Explanation
Two events are mutually exclusive if they cannot happen together. For such events, the OR probability is the sum of individual probabilities.
Key Formula
- P(A or B) = P(A) + P(B) when A and B are mutually exclusive
- On one die roll, getting 2 and getting 5 are mutually exclusive
- Mutually exclusive events are not independent (unless one has P = 0)
Example
One die: P(2 or 5) = 1/6 + 1/6 = 1/3.
Common Trap
Do not add probabilities if events can overlap.
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Q1 EasyA fair die is rolled once. What is P(getting 1 or 6)?ExplanationThe faces 1 and 6 cannot occur together, so they are mutually exclusive. P = 1/6 + 1/6 = 1/3. Hence the answer is 1/3.
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Q2 EasyOne card is drawn from a pack of 52. What is P(heart or diamond)?ExplanationHearts and diamonds are different suits, so mutually exclusive. P = 13/52 + 13/52 = 26/52 = 1/2. Hence the answer is 1/2.
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Q3 EasyIf P(A) = 1/4, P(B) = 1/3 and A, B are mutually exclusive, what is P(A or B)?ExplanationFor mutually exclusive events, P(A ∪ B) = P(A) + P(B) = 1/4 + 1/3 = 3/12 + 4/12 = 7/12. Hence the answer is 7/12.
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Q4 EasyA fair die is thrown. What is the probability of getting 2 or 5?ExplanationOutcomes 2 and 5 are mutually exclusive. P = 1/6 + 1/6 = 1/3. Hence the answer is 1/3.
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Q5 MediumTickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?ExplanationMultiples of 3: 3,6,9,12,15,18 (6 numbers). Multiples of 5: 5,10,15,20 (4 numbers). Overlap (multiple of 15): 15 (1 number). Favourable = 6 + 4 − 1 = 9. P = 9/20. Hence the answer is 9/20.
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Q6 MediumA bag has 5 red, 3 blue and 2 green balls. One ball is drawn. What is P(red or blue)?ExplanationRed and blue cannot occur on the same single draw. Favourable = 5 + 3 = 8 out of 10. P = 8/10 = 4/5. Hence the answer is 4/5.
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Q7 MediumAn HR quiz states P(A) = 1/5 and P(B) = 2/5, and A and B cannot occur together. What is P(A or B)?ExplanationCannot occur together means mutually exclusive, so P(A ∪ B) = 1/5 + 2/5 = 3/5. Hence the answer is 3/5.
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Q8 MediumTwo events A and B cannot occur together. If P(A) = 0.35 and P(B) = 0.25, what is P(A ∪ B)?ExplanationCannot occur together ⇒ mutually exclusive ⇒ P(A ∪ B) = P(A) + P(B) = 0.35 + 0.25 = 0.60. Hence the answer is 0.60.
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Q9 MediumOne card is drawn. What is P(club or spade)?ExplanationClubs and spades are mutually exclusive black suits. P = 13/52 + 13/52 = 1/2. Hence the answer is 1/2.
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Q10 MediumOne card is drawn from a pack of 52 cards. What is the probability of getting a king or a queen?ExplanationA card cannot be both king and queen. Favourable = 4 + 4 = 8. P = 8/52 = 2/13. Hence the answer is 2/13.
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Q11 MediumA fair die is rolled. What is P(even or 5)?ExplanationEven faces {2,4,6} and face 5 are mutually exclusive. Favourable = 4 outcomes. P = 4/6 = 2/3. Hence the answer is 2/3.
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Q12 HardOne card is drawn. What is P(ace or face card)?ExplanationAces and face cards (J, Q, K) are disjoint ranks: 4 + 12 = 16 cards. P = 16/52 = 4/13. Hence the answer is 4/13.
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Q13 HardA speaks truth in 75% of cases and B in 80% of cases. The probability that they contradict each other in describing the same event is:ExplanationThey contradict when (A true, B false) or (A false, B true). These cases are mutually exclusive. P = (3/4)(1/5) + (1/4)(4/5) = 3/20 + 4/20 = 7/20. Hence the answer is 7/20.
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Q14 HardP(A) = 0.25, P(B) = 0.35 and A, B are mutually exclusive. What is P(neither A nor B)?ExplanationP(A ∪ B) = 0.25 + 0.35 = 0.60. P(neither) = 1 − 0.60 = 0.40. Hence the answer is 0.40.
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DS1 Easy
In a campus probability drill, what is P(A ∪ B) when A and B are mutually exclusive?
Statement IP(A) = 0.2.
Statement IIP(B) = 0.5 and A, B are mutually exclusive.
ExplanationStatement I alone lacks P(B) and exclusivity. Statement II alone lacks P(A). Together: P(A ∪ B) = 0.2 + 0.5 = 0.7. Answer: C. -
DS2 Easy
What is P(getting 2 or 5 on one die roll)?
Statement IA fair six-sided die is rolled once.
Statement IIThe outcomes 2 and 5 cannot occur together.
ExplanationNeed fairness (equal faces) and mutual exclusivity to add: P = 1/6 + 1/6 = 1/3. Answer: C.
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DS3 Medium
For P(king or queen on one draw from a 52-card deck). Can it be found?
Statement IThere are 4 kings and 4 queens in the deck.
Statement IIA single card cannot be both a king and a queen.
ExplanationStatement I gives counts but needs exclusivity to add without overlap. Statement II alone lacks counts. Together: P = 8/52 = 2/13. Answer: C. -
DS4 Hard
A placement worksheet asks: A speaks truth in 75% of cases and B in 80%. What is P(they contradict each other)?
Statement IContradiction means exactly one of them tells the truth.
Statement IITheir truth-telling events are independent.
ExplanationNeed both the exclusive cases interpretation and independence: P = (3/4)(1/5) + (1/4)(4/5) = 7/20. Answer: C.