Theoretical DistributionsMCQPYQ Dec 21Question 3424 of 230
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Four unbiased coins are tossed simultaneously. The expected no. of heads is:

Options

A1\displaystyle 1
B2\displaystyle 2
C3\displaystyle 3
D4\displaystyle 4
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Correct Answer

✅ Option b — 2\displaystyle 2

All Options:

  • A1\displaystyle 1
  • B2\displaystyle 2
  • C3\displaystyle 3
  • D4\displaystyle 4

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Detailed Solution & Explanation

Given:4unbiasedcoinsaretossedsimultaneously.\n\nStep1:Identifytheparameters.\nThisfollowsaBinomialdistributionwhere:\n−n=4(numberofcoins)\n−p=1/2(probabilityofheadoneachcoin,sincecoinsareunbiased)\n−q=1−1/2=1/2\n\nStep2:ApplytheformulaforExpectedValue(Mean).\nE(X)=np\n\nStep3:Substitutethevalues.\nE(X)=4timesfrac12=2\n\nTherefore,theexpectednumberofheads=2.\n\nHence,∗∗OptionB∗∗isthecorrectanswer.\displaystyle Given: 4 unbiased coins are tossed simultaneously.\n\nStep 1: Identify the parameters.\nThis follows a Binomial distribution where:\n- n = 4 (number of coins)\n- p = 1/2 (probability of head on each coin, since coins are unbiased)\n- q = 1 - 1/2 = 1/2\n\nStep 2: Apply the formula for Expected Value (Mean).\nE(X) = np\n\nStep 3: Substitute the values.\nE(X) = 4 \\times \\frac{1}{2} = 2\n\nTherefore, the expected number of heads = 2.\n\nHence, **Option B** 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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