Practice Questions
Concept Explanation
A fair coin has two equally likely outcomes: heads (H) and tails (T). Tossing multiple coins multiplies the number of outcomes.
Key Rules
- One coin: P(H) = P(T) = 1/2
- Two coins: 4 outcomes — HH, HT, TH, TT
- n coins: 2n outcomes (when order matters)
Example
Two fair coins: P(both heads) = 1/4; P(at least one head) = 3/4.
Common Trap
HT and TH are different outcomes when order is recorded.
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Q1 Easy
One fair coin is tossed. What is P(tails)?
ExplanationP(T) = 1/2 for a fair coin. -
Q2 Easy
Two fair coins are tossed. How many outcomes?
ExplanationHH, HT, TH, TT: 4 outcomes. -
Q3 Easy
Two fair coins tossed. What is P(both heads)?
ExplanationOnly HH: P = 1/4. -
Q4 Medium
Two fair coins tossed. What is P(at least one head)?
ExplanationExclude TT: P = 3/4. -
Q5 Medium
Two fair coins tossed. What is P(exactly one head)?
ExplanationHT and TH: P = 2/4 = 1/2. -
Q6 Easy
Three fair coins tossed. How many outcomes?
Explanation2^3 = 8 outcomes. -
Q7 Easy
Three fair coins tossed. What is P(all heads)?
ExplanationOnly HHH: P = 1/8.
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Q8 Medium
Three fair coins tossed. What is P(at least one tail)?
Explanation1 − P(all heads) = 1 − 1/8 = 7/8. -
Q9 Medium
Three fair coins tossed. What is P(exactly two heads)?
ExplanationHHT, HTH, THH: P = 3/8. -
Q10 Hard
Four fair coins tossed. What is P(no heads)?
ExplanationAll tails: P = (1/2)^4 = 1/16. -
Q11 Easy
Two fair coins tossed. What is P(both tails)?
ExplanationOnly TT: P = 1/4. -
Q12 Hard
Three fair coins tossed. What is P(exactly one head)?
ExplanationHTT, THT, TTH: P = 3/8. -
Q13 Medium
Five fair coins tossed. How many outcomes?
Explanation2^5 = 32 outcomes. -
Q14 Medium
Two fair coins tossed. What is P(different results)?
ExplanationHT or TH: P = 2/4 = 1/2.
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DS1 Easy
What is P(both heads when two fair coins are tossed)?
Statement ITwo fair coins are tossed.
Statement IIThere are 4 equally likely outcomes.
ExplanationNeed both: P = 1/4. -
DS2 Medium
What is P(at least one head when two coins are tossed)?
Statement ITwo fair coins are tossed.
Statement IIP(both tails) = 1/4.
ExplanationStatement II alone: P = 1 − 1/4 = 3/4.
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DS3 Easy
How many outcomes when three fair coins are tossed?
Statement IEach coin has 2 outcomes.
Statement IIThree coins are tossed.
ExplanationNeed both: 2^3 = 8 outcomes. -
DS4 Medium
What is P(all heads when four coins are tossed)?
Statement IFour fair coins are tossed.
Statement IIP(all heads) = 1/16.
ExplanationEach alone gives P = 1/16.