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 Easy
One die rolled. What is P(2 or 5)?
ExplanationMutually exclusive: 1/6 + 1/6 = 1/3. -
Q2 Easy
One card drawn. What is P(heart or spade)?
ExplanationDifferent suits: 13/52 + 13/52 = 1/2. -
Q3 Easy
One die rolled. What is P(1 or 6)?
Explanation1/6 + 1/6 = 1/3. -
Q4 Medium
Bag: 4 red, 3 blue, 3 green. What is P(red or blue)?
Explanation(4+3)/10 = 7/10. -
Q5 Easy
P(A) = 0.3, P(B) = 0.4, mutually exclusive. P(A or B)?
ExplanationP = 0.3 + 0.4 = 0.7. -
Q6 Medium
One card drawn. What is P(king or queen)?
Explanation8 cards: P = 8/52 = 2/13. -
Q7 Medium
One die rolled. What is P(even or 5)?
ExplanationEven: 2,4,6 plus 5: 4/6 = 2/3.
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Q8 Medium
P(A) = 1/4, P(B) = 1/3, mutually exclusive. P(A or B)?
Explanation1/4 + 1/3 = 7/12. -
Q9 Hard
One card drawn. What is P(ace or face card)?
Explanation4 aces + 12 faces = 16 cards. P = 16/52 = 4/13. -
Q10 Easy
Bag: 2 red, 2 blue balls. What is P(red or blue on one draw)?
ExplanationEvery ball is red or blue: P = 1. -
Q11 Easy
One die rolled. What is P(3 or 4 or 5)?
Explanation3/6 = 1/2. -
Q12 Hard
P(A) = 0.25, P(B) = 0.35, mutually exclusive. P(neither)?
ExplanationP(A or B) = 0.6; P(neither) = 0.4. -
Q13 Medium
One card drawn. What is P(club or diamond)?
ExplanationRed suits total 26: P = 1/2. -
Q14 Easy
Two dice rolled. Is getting sum 7 and sum 8 on the same roll possible?
ExplanationOne roll has one sum; events are mutually exclusive.
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DS1 Easy
What is P(A or B) if A and B are mutually exclusive?
Statement IP(A) = 0.2.
Statement IIP(B) = 0.5 and A, B are mutually exclusive.
ExplanationNeed both: P = 0.2 + 0.5 = 0.7. -
DS2 Easy
What is P(2 or 5 on one die roll)?
Statement IA fair die is rolled once.
Statement IIOutcomes 2 and 5 cannot occur together.
ExplanationNeed both: P = 1/6 + 1/6 = 1/3.
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DS3 Medium
What is P(heart or spade on one card draw)?
Statement IOne card is drawn from a 52-card deck.
Statement IIHearts and spades are different suits.
ExplanationNeed both: P = 13/52 + 13/52 = 1/2. -
DS4 Medium
What is P(king or queen on one card draw)?
Statement IThere are 4 kings and 4 queens.
Statement IIA single card cannot be both king and queen.
ExplanationNeed both: P = 8/52 = 2/13.