Theoretical DistributionsPYQ May 25Question 4088 of 230
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What is the probability of making 3 corrected guesses in 5 True-False answer type questions?

Options

A0.3125
B0.4156
C1.3888
D0.5235
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Correct Answer

✅ Option a — 0.3125

All Options:

  • A0.3125
  • B0.4156
  • C1.3888
  • D0.5235

Detailed Solution & Explanation

This problem can be modeled using the Binomial Distribution:
Let:
- Number of trials (questions) n=5\displaystyle n = 5.
- Probability of guessing a True-False question correctly p=12=0.5\displaystyle p = \frac{1}{2} = 0.5.
- Probability of guessing incorrectly q=1−p=0.5\displaystyle q = 1 - p = 0.5.
- Number of successful guesses x=3\displaystyle x = 3.

The probability mass function of a Binomial distribution is given by:
P(X=x)=(nx)pxqn−xP(X = x) = \binom{n}{x} p^x q^{n - x} Substituting the values:
P(X=3)=(53)(0.5)3(0.5)5−3P(X = 3) = \binom{5}{3} (0.5)^3 (0.5)^{5 - 3} P(X=3)=(53)(0.5)5P(X = 3) = \binom{5}{3} (0.5)^5 Calculate the combination and power:
(53)=5×42×1=10\binom{5}{3} = \frac{5 \times 4}{2 \times 1} = 10 (0.5)5=0.03125(0.5)^5 = 0.03125 Substitute these values:
P(X=3)=10×0.03125=0.3125P(X = 3) = 10 \times 0.03125 = 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.

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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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