Theoretical DistributionsMCQMTP March 22Question 3455 of 230
All Questions

What is the probability of getting 3 heads if 6 unbiased coins are tossed simultaneously?

Options

A0.3125
B0.25
C0.6825
D0.50
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Correct Answer

✅ Option a — 0.3125

All Options:

  • A0.3125
  • B0.25
  • C0.6825
  • D0.50

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Detailed Solution & Explanation

Here n=6\displaystyle n = 6 (number of coins), p=12\displaystyle p = \frac{1}{2} (probability of head), q=12\displaystyle q = \frac{1}{2}, and r=3\displaystyle r = 3. Using the binomial probability formula: P(X=3)=(63)(12)3(12)3P(X = 3) = \binom{6}{3} \left(\frac{1}{2}\right)^3 \left(\frac{1}{2}\right)^3 =(63)(12)6= \binom{6}{3} \left(\frac{1}{2}\right)^6 =20×164= 20 \times \frac{1}{64} =2064=0.3125= \frac{20}{64} = 0.3125 Hence, **Option A** 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.

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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A random variable X\displaystyle X follows Binomial Distribution With E(x)=2\displaystyle E(x)=2 and V(x)=1.2\displaystyle V(x)=1.2, then the value of n\displaystyle n is

When 'p\displaystyle p' is large than 0.5\displaystyle 0.5, the Binomial Distribution is:

For a Poisson distribution,

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