Check sibling questions

Example 25 - Find probability distribution of number of doublets in 3

Example 25 - Chapter 13 Class 12 Probability - Part 2
Example 25 - Chapter 13 Class 12 Probability - Part 3
Example 25 - Chapter 13 Class 12 Probability - Part 4
Example 25 - Chapter 13 Class 12 Probability - Part 5

Solve all your doubts with Teachoo Black (new monthly pack available now!)


Transcript

Example 25 Find the probability distribution of number of doublets in three throws of a pair of dice. If 2 dies are thrown, there are 6 × 6 = 36 outcomes Doublet: It means same number is obtained on both throws of die Number of doublets possible on 2 throws of die are (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6) P(getting a doublet) = 6/36 = 1/6 P(not getting a doublet) = 1 – 1/6 = 5/6 We need to find probability distribution of number of doublets in three throws of a pair of dice. Since Two dies are thrown thrice. We can get, 0 doublet or 1 doublet or 2 doublets or 3 doublets So, value of X can be 0, 1, 2, 3 P(X = 0) P(X = 0) = P(0 doublet on three throws) = P(0 doublet) × P(0 doublet) × P(0 doublet) = 5/6 × 5/6 × 5/6 = 125/216 P(X = 1) P(X = 1) = P(one doublet on three throws) = P(one doublet) × P(0 doublet) × P(0 doublet) + P(0 doublet) × P(one doublet) × P(0 doublet) + P(0 doublet) × P(0 doublet) × P(one doublet) = 1/6 × 5/6 × 5/6 + 5/6 × 1/6 × 5/6 + 5/6 × 5/6 × 1/6 = 3 × 5/6 × 5/6 × 1/6 = 75/216 P(X = 2) P(X = 2) = P(two doublet on three throws) = P(one doublet) × P(one doublet) × P(0 doublet) + P(one doublet) × P(0 doublet) × P(one doublet) + P(0 doublet) × P(one doublet) × P(one doublet) = 1/6 × 1/6 × 5/6 + 1/6 × 5/6 × 1/6 + 5/6 × 1/6 × 1/6 = 3 × 1/6 × 1/6 × 5/6 = 15/216 P(X = 3) P(X = 3) = P(three doublets on three throws) = P(one doublet) × P(one doublet) × P(one doublet) = 1/6 × 1/6 × 1/6 = 1/216 So, probability distribution is

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.