Question 27 (Choice 2) - CBSE Class 12 Sample Paper for 2023 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at March 22, 2023 by Teachoo

Find the mean number of defective items in a sample of two items drawn one-by-one without replacement from an urn containing 6 items, which include 2 defective items. Assume that the items are identical in shape and size.

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Question 27 (Choice 2) Find the mean number of defective items in a sample of two items drawn one-by-one without replacement from an urn containing 6 items, which include 2 defective items. Assume that the items are identical in shape and size.
Let X : Number of defective items drawn
Since there are maximum of 2 defective items
We can get 0, 1 or 2 defective items
So, X = 0 or X = 1 or X = 2
Finding probabilities separately
For X = 0
Two items drawn, without replacement, 0 are defective
P(X = 0) = P(not defective) × P(not defective)
= 4/6 × 3/5
= 𝟐/𝟓
For X = 1
Two items drawn, without replacement, 1 is defective
P(X = 1) = P(not defective) × P(defective) + P(defective) × P(not defective)
= 𝟒/𝟔 × 𝟐/𝟓 + 𝟐/𝟔 × 𝟒/𝟓
= 8/30+8/30
= 16/30
= 𝟖/𝟏𝟓
For X = 2
Two items drawn, without replacement, 2 are defective
P(X = 2) = P(defective) × P(defective)
= 2/6 × 1/5
= 𝟏/𝟏𝟓
So, probability distribution is
Now,
We need to find Mean or Expectation of X
Mean or Expectation of X
= E(X)
= ∑_(𝒊 = 𝟏)^𝒏▒𝒙𝒊𝒑𝒊
= 0 ×2/5+1 × 8/15+2 × 1/15
= 8/15+ 2/15
= 10/15
= 𝟐/𝟑

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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