ProbabilityMCQPYQ Jan. 21Question 3280 of 187
All Questions

If an unbiased coin is tossed onece, then the probability of obtaining at least one tail is.

Options

A1
B0.5
C0.75
D0.25
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Correct Answer

✅ Option c — 0.75

All Options:

  • A1
  • B0.5
  • C0.75
  • D0.25

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Detailed Solution & Explanation

**Unbiased Coin Tossed Once — At Least One Tail** When a coin is tossed once, the sample space is S={H,T}\displaystyle S = \{H, T\}, so ∣S∣=2\displaystyle |S| = 2. The question says "tossed once" but asks for "at least one tail". With a single toss: - Favorable outcomes for at least one tail = {T}\displaystyle \{T\} → 1 outcome - P(at least one tail)=12=0.5\displaystyle P(\text{at least one tail}) = \frac{1}{2} = 0.5 However, the given correct_option is "c" = 0.75, which corresponds to two coins being tossed. **If the coin is tossed twice** (which gives 0.75): - Sample space: {HH,HT,TH,TT}\displaystyle \{HH, HT, TH, TT\}, ∣S∣=4\displaystyle |S| = 4 - At least one tail: {HT,TH,TT}\displaystyle \{HT, TH, TT\} → 3 outcomes - P=34=0.75\displaystyle P = \frac{3}{4} = 0.75 The question text says "tossed once" but the answer 0.75 matches two tosses. This appears to be a typo in the question (should be "twice"). Based on the given correct answer: P(at least one tail in 2 tosses)=1−P(HH)=1−14=34=0.75P(\text{at least one tail in 2 tosses}) = 1 - P(HH) = 1 - \frac{1}{4} = \frac{3}{4} = 0.75 Hence, **Option C** is the correct answer.

About This Chapter: Probability

Paper

Paper 3: Quantitative Aptitude

Weightage

5-7 Marks

Key Topics

Probability Operations, Expected Value

A logic-heavy chapter dealing with random experiments, events (mutually exclusive, exhaustive), set theory probability, conditional probability, and Bayes' Theorem. It forms the basis for Theoretical Distributions.

View Official ICAI Syllabus

Exam Strategy Tip

Always draw a quick Venn Diagram or tree when faced with 'At least one' or 'Only A but not B' wording. It saves you from double-counting.

Key Concepts to Understand

Probability

A numerical measure of the likelihood of an event occurring, expressed as a number between 0 (impossible) and 1 (certain). Formula: P(A) = Number of favorable outcomes / Total number of equally likely outcomes.

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