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Match list I with list II. 4 defective pens are mixed with 10 normal pens. 3 pens are drawn one by one with replacement , then the probability distribution of the number of defective pens is :

List-IList - II
A. P(X=0)8/343
B. P(X=1)60/343
C. P(X=2)125/343
D. P(X=3)150/343

Choose the correct option below :

Solution

✅ Correct Option: 2

Total pens = 14. With replacement, p=414=27p = \frac{4}{14} = \frac{2}{7}, q=57q = \frac{5}{7}, n=3n = 3.

P(X=0)=(5/7)3=125/343P(X=0) = (5/7)^3 = 125/343 (matches row III).

P(X=1)=3(2/7)(5/7)2=150/343P(X=1) = 3(2/7)(5/7)^2 = 150/343 (matches row IV).

P(X=2)=3(2/7)2(5/7)=60/343P(X=2) = 3(2/7)^2(5/7) = 60/343 (matches row II).

P(X=3)=(2/7)3=8/343P(X=3) = (2/7)^3 = 8/343 (matches row I).

Match: A-III, B-IV, C-II, D-I.

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