Theoretical DistributionsMCQPYQ Dec 23Question 3428 of 230
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If mean and variance of a random variable which follows the Binomial Distribution are 7\displaystyle 7 and 6\displaystyle 6 respectively, then the probability of success is:

Options

A67\displaystyle \frac{6}{7}
B3649\displaystyle \frac{36}{49}
C17\displaystyle \frac{1}{7}
D149\displaystyle \frac{1}{49}
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Correct Answer

✅ Option c — 17\displaystyle \frac{1}{7}

All Options:

  • A67\displaystyle \frac{6}{7}
  • B3649\displaystyle \frac{36}{49}
  • C17\displaystyle \frac{1}{7}
  • D149\displaystyle \frac{1}{49}

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Detailed Solution & Explanation

Given:Mean=np=7andVariance=npq=6.\n\nStep1:Findqusingtherelationshipbetweenvarianceandmean.\nfractextVariancetextMean=fracnpqnp=q\n\nq=frac67\n\nStep2:Findp.\np=1−q=1−frac67=frac17\n\nStep3:Verification.\nn=fractextMeanp=frac71/7=49\nnpq=49timesfrac17timesfrac67=7timesfrac67=6✓\n\nTherefore,p=frac17.\n\nHence,∗∗OptionC∗∗isthecorrectanswer.\displaystyle Given: Mean = np = 7 and Variance = npq = 6.\n\nStep 1: Find q using the relationship between variance and mean.\n\\frac{\\text{Variance}}{\\text{Mean}} = \\frac{npq}{np} = q\n\nq = \\frac{6}{7}\n\nStep 2: Find p.\np = 1 - q = 1 - \\frac{6}{7} = \\frac{1}{7}\n\nStep 3: Verification.\nn = \\frac{\\text{Mean}}{p} = \\frac{7}{1/7} = 49\nnpq = 49 \\times \\frac{1}{7} \\times \\frac{6}{7} = 7 \\times \\frac{6}{7} = 6 ✓\n\nTherefore, p = \\frac{1}{7}.\n\nHence, **Option C** 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.

Variance

A measure of dispersion equal to the average of the squared deviations of each data point from the mean. Formula: σ² = Σ(xᵢ − x̄)² / n. Standard Deviation = √Variance.

More Questions from Theoretical Distributions

Find the variance of binomial distribution with n=10\displaystyle n=10, p=0.3\displaystyle p=0.3

When p=0.5\displaystyle p=0.5, the binomial distribution is

If mean and standard deviation of a binomial distribution is 10\displaystyle 10 and 2\displaystyle 2 respectively, q\displaystyle q will be

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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