Theoretical DistributionsMCQMTP Nov 19Question 3442 of 230
All Questions

Five coins tossed 3200 times. The number of times 5 heads appeared is.

Options

A500
B1200
C200
D100
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Correct Answer

✅ Option d — 100

All Options:

  • A500
  • B1200
  • C200
  • D100

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Detailed Solution & Explanation

**Expected Number of Times 5 Heads Appear**\n\nGiven: 5 fair coins tossed, experiment repeated 3200 times.\n\n**Step 1: Probability of getting 5 heads in one toss**\n\nEach coin: P(textHead)=frac12\displaystyle P(\\text{Head}) = \\frac{1}{2}, n=5\displaystyle n = 5\nP(X=5)=binom55left(frac12right)5left(frac12right)0=1timesfrac132=frac132P(X = 5) = \\binom{5}{5} \\left(\\frac{1}{2}\\right)^5 \\left(\\frac{1}{2}\\right)^0 = 1 \\times \\frac{1}{32} = \\frac{1}{32}\n\n**Step 2: Expected number of times**\ntextExpectedfrequency=NtimesP(X=5)=3200timesfrac132=100\\text{Expected frequency} = N \\times P(X = 5) = 3200 \\times \\frac{1}{32} = 100\n\n> **Note:** The correct answer is **100** (Option D). The textbook answer key lists Option B (1200), which is incorrect.\n\nHence, **Option D** is the correct answer.

About This Chapter: Theoretical Distributions

Paper

Paper 3: Quantitative Aptitude

Weightage

4-6 Marks

Key Topics

Binomial, Poisson, Normal Distribution

This chapter covers Binomial, Poisson, Normal Distribution and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

View Official ICAI Syllabus

Exam Strategy Tip

This topic carries 4-6 Marks weightage. Focus on understanding core concepts rather than memorizing.

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