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 EasyOne fair coin is tossed. What is the probability of getting tails?ExplanationP(E) = favourable / total. Outcomes: H, T → 2 equally likely. Favourable (T) = 1. P = 1/2. Hence the answer is 1/2.
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Q2 EasyTwo fair coins are tossed. How many outcomes are possible?ExplanationOrdered outcomes: HH, HT, TH, TT → 4. Hence the answer is 4.
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Q3 EasyTwo fair coins are tossed. What is the probability that the two coins show different faces?ExplanationP(E) = favourable / total. Different faces: HT, TH → 2 out of 4. P = 2/4 = 1/2. Hence the answer is 1/2.
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Q4 EasyThree coins are tossed. What is the probability of getting no heads?ExplanationP(E) = favourable / total. No heads means all tails: TTT only → 1 out of 8. P = 1/8. Hence the answer is 1/8.
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Q5 EasyThree coins are tossed. What is the probability of getting all heads?ExplanationP(E) = favourable / total. All heads: HHH only → 1 out of 8. P = 1/8. Hence the answer is 1/8.
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Q6 EasyTwo coins are tossed. What is the probability of getting two heads?ExplanationP(E) = favourable / total. Outcomes: HH, HT, TH, TT → 4. Favourable (two heads): HH → 1. P = 1/4. Hence the answer is 1/4.
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Q7 MediumThree unbiased coins are tossed. What is the probability of getting at least two heads?ExplanationP(E) = favourable / total. Total outcomes = 2^3 = 8. Favourable (at least 2 heads): HHH, HHT, HTH, THH → 4. P = 4/8 = 1/2. Hence the answer is 1/2.
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Q8 MediumTwo coins are tossed. The probability of getting at least one head is:ExplanationP(E) = favourable / total. Outcomes: HH, HT, TH, TT → 4. Favourable (at least one head): HH, HT, TH → 3. P = 3/4. Equivalently 1 − P(TT) = 1 − 1/4 = 3/4. Hence the answer is 3/4.
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Q9 MediumThree coins are tossed. What is the probability of getting exactly two heads?ExplanationP(E) = favourable / total. Total = 8. Exactly two heads: HHT, HTH, THH → 3. P = 3/8. Hence the answer is 3/8.
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Q10 MediumTwo fair coins are tossed. What is the probability of getting exactly one head?ExplanationP(E) = favourable / total. Exactly one head: HT, TH → 2 out of 4. P = 2/4 = 1/2. Hence the answer is 1/2.
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Q11 MediumThree fair coins are tossed. What is the probability of getting at least one tail?ExplanationP(E) = 1 − P(no tail) = 1 − P(all heads) = 1 − 1/8 = 7/8. Favourable count: 7 of 8 outcomes have at least one T. Hence the answer is 7/8.
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Q12 MediumFive fair coins are tossed. How many outcomes are in the sample space?Explanationn(S) = 2^5 = 32. Hence the answer is 32.
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Q13 HardFour fair coins are tossed. What is the probability of getting no heads?ExplanationP(E) = favourable / total. Total = 2^4 = 16. No heads = TTTT → 1. P = 1/16. Hence the answer is 1/16.
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Q14 HardThree fair coins are tossed. What is the probability of getting exactly one head?ExplanationP(E) = favourable / total. Exactly one head: HTT, THT, TTH → 3 out of 8. P = 3/8. Hence the answer is 3/8.
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DS1 Easy
What is the probability of getting both heads when two fair coins are tossed?
Statement ITwo fair coins are tossed.
Statement IIThere are 4 equally likely outcomes: HH, HT, TH and TT.
ExplanationStatement I alone does not enumerate the outcomes. Statement II alone does not identify how many of those outcomes are both heads without the question context of fairness — together with the question: favourable = 1 (HH), total = 4, P = 1/4. Both needed. Answer: C. -
DS2 Easy
How many outcomes occur when three fair coins are tossed. What is that number?
Statement IEach coin has 2 equally likely outcomes.
Statement IIThree fair coins are tossed independently.
ExplanationStatement I alone lacks the number of coins. Statement II alone lacks the per-coin outcome count. Together: 2^3 = 8. Both needed. Answer: C.
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DS3 Medium
What is the probability of getting at least one head when two coins are tossed?
Statement ITwo fair coins are tossed.
Statement IIThe probability of both tails is 1/4.
ExplanationStatement I alone requires enumerating outcomes to finish. Statement II alone: P(at least one head) = 1 − P(both tails) = 1 − 1/4 = 3/4. Answer: B. -
DS4 Medium
For the probability of all heads when four fair coins are tossed. What is that probability?
Statement IFour fair coins are tossed.
Statement IIP(all heads) equals (1/2)^4.
ExplanationStatement I alone: only HHHH of 16 outcomes → P = 1/16. Statement II alone: (1/2)^4 = 1/16. Each alone is sufficient. Answer: D.