CBSE Class 12 Sample Paper for 2022 Boards (For Term 2)

Class 12
Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

## A bag contains 1 red and 3 white balls. Find the probability distribution of the number of red balls if 2 balls are drawn at random from the bag one-by-one without replacement.

### Transcript

Question 5 A bag contains 1 red and 3 white balls. Find the probability distribution of the number of red balls if 2 balls are drawn at random from the bag one-by-one without replacement. Let X: Number of red balls drawn Since there is only 1 red ball So, we can get 0 red balls or 1 red ball ∴ Value of X can be 0, 1 Finding P(X = 0) i.e. Probability that 0 red balls are drawn ½ marks P(X = 0) = Probability that 0 red balls are drawn = Probability that 1st ball drawn is white × Probability that 2nd ball drawn is white = 3/4 ×2/3 = 𝟏/𝟐 Finding P(X = 1) i.e. Probability that 1 red ball is drawn P(X = 1) = Probability that 1 red balls are drawn = Probability that 1st ball drawn is red × Probability that 2nd ball drawn is white + Probability that 1st ball drawn is white × Probability that 2nd ball drawn is red ½ marks = 𝟏/𝟒 ×𝟑/𝟑+𝟑/𝟒 ×𝟏/𝟑 = 1/4+1/4 = 𝟏/𝟐 So, our probability distribution is

#### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.