The incidence of skin diseases in a chemical plant occurs in such a way that the workers have 20% chance of suffering from it. What is the probability that out of 6 workers 4 or more will have skin diseases?

Option b: 0.01696. Solution: Given: p = 0.2, q = 1 - 0.2 = 0.8, n = 6. need P(X ≥ 4) = P(X=4) + P(X=5) + P(X=6). the Binomial formula: P(X = r) = (n choose r) pr qn-r 1: Calculate P(X = 4).(X=4) = (6 choose 4) (0.2)4 (0.8)2= 15 × 0.0016 × 0.64= 15 × 0.001024= 0.015360 2: Calculate P(X = 5).(X=5) = (6 choose 5) (0.2)5 (0.8)1= 6 × 0.00032 × 0.8= 6 × 0.000256= 0.001536 3: Calculate P(X = 6).(X=6) = (6 choose 6) (0.2)6 (0.8)0= 1 × 0.000064 × 1= 0.000064 4: Add all probabilities.(X ≥ 4) = 0.015360 + 0.001536 + 0.000064= 0.016960= 0.01696, Option B is the correct answer.

Theoretical DistributionsMCQPYQ Jun 23Question 3427 of 230

All Questions

The incidence of skin diseases in a chemical plant occurs in such a way that the workers have $\displaystyle 20\%$ chance of suffering from it. What is the probability that out of $\displaystyle 6$ workers $\displaystyle 4$ or more will have skin diseases?

Options

\displaystyle 0.1696

\displaystyle 0.01696

\displaystyle 0.1643

\displaystyle 0.01643

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Correct Answer

✅ Option b — $\displaystyle 0.01696$

All Options:

A $\displaystyle 0.1696$
B $\displaystyle 0.01696$
C $\displaystyle 0.1643$
D $\displaystyle 0.01643$

Detailed Solution & Explanation

\displaystyle Given: p = 0.2, q = 1 - 0.2 = 0.8, n = 6.\nWe need P(X \\geq 4) = P(X=4) + P(X=5) + P(X=6).\n\nUsing the Binomial formula: P(X = r) = \\binom{n}{r} p^r q^{n-r}\n\nStep 1: Calculate P(X = 4).\nP(X=4) = \\binom{6}{4} (0.2)^4 (0.8)^2\n= 15 \\times 0.0016 \\times 0.64\n= 15 \\times 0.001024\n= 0.015360\n\nStep 2: Calculate P(X = 5).\nP(X=5) = \\binom{6}{5} (0.2)^5 (0.8)^1\n= 6 \\times 0.00032 \\times 0.8\n= 6 \\times 0.000256\n= 0.001536\n\nStep 3: Calculate P(X = 6).\nP(X=6) = \\binom{6}{6} (0.2)^6 (0.8)^0\n= 1 \\times 0.000064 \\times 1\n= 0.000064\n\nStep 4: Add all probabilities.\nP(X \\geq 4) = 0.015360 + 0.001536 + 0.000064\n= 0.016960\n= 0.01696\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.

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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The incidence of skin diseases in a chemical plant occurs in such a way that the workers have 20%\displaystyle 20\%20% chance of suffering from it. What is the probability that out of 6\displaystyle 66 workers 4\displaystyle 44 or more will have skin diseases?