ProbabilityMCQPYQ June 19Question 3316 of 187
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If a coin is tossed 5\displaystyle 5 times then the probability of getting Tail and Head occurs alternatively is

Options

A18\displaystyle \frac{1}{8}
B116\displaystyle \frac{1}{16}
C132\displaystyle \frac{1}{32}
D164\displaystyle \frac{1}{64}
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Correct Answer

✅ Option b — 116\displaystyle \frac{1}{16}

All Options:

  • A18\displaystyle \frac{1}{8}
  • B116\displaystyle \frac{1}{16}
  • C132\displaystyle \frac{1}{32}
  • D164\displaystyle \frac{1}{64}

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Detailed Solution & Explanation

**Probability of Alternating Heads and Tails in 5 Tosses** Total outcomes = 25=32\displaystyle 2^5 = 32 Alternating sequences of length 5 (H and T alternate): 1. Starting with H: H,T,H,T,H\displaystyle H, T, H, T, H — 1 sequence 2. Starting with T: T,H,T,H,T\displaystyle T, H, T, H, T — 1 sequence Total favorable = **2** P(alternating)=232=116P(\text{alternating}) = \frac{2}{32} = \frac{1}{16} Hence, **Option B** 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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