Theoretical DistributionsMCQMTP May 20Question 3444 of 230
All Questions

An experiment succeeds thrice as after it fails. If the experiment is repeated 5times, what is the probability of having no success at all?

Options

A1/1023\displaystyle 1/1023
B1/1024\displaystyle 1/1024
C1/1005\displaystyle 1/1005
D1/1000\displaystyle 1/1000
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Correct Answer

✅ Option b — 1/1024\displaystyle 1/1024

All Options:

  • A1/1023\displaystyle 1/1023
  • B1/1024\displaystyle 1/1024
  • C1/1005\displaystyle 1/1005
  • D1/1000\displaystyle 1/1000

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Detailed Solution & Explanation

**Probability of No Success in 5 Trials** **Setting up probabilities:** The experiment succeeds 3 times as often as it fails: fracpq=3Rightarrowp=3q\\frac{p}{q} = 3 \\Rightarrow p = 3q Using p+q=1\displaystyle p + q = 1: 3q+q=1Rightarrow4q=1Rightarrowq=frac14, p=frac343q + q = 1 \\Rightarrow 4q = 1 \\Rightarrow q = \\frac{1}{4},\ p = \\frac{3}{4} **Probability of no success in 5 trials:** P(X=0)=binom50p0q5=q5P(X = 0) = \\binom{5}{0} p^0 q^5 = q^5 P(X=0)=left(frac14right)5=frac145=frac11024P(X = 0) = \\left(\\frac{1}{4}\\right)^5 = \\frac{1}{4^5} = \\frac{1}{1024} Hence, **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.

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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