Note:-This question is exactly same as Example 5

Last updated at May 25, 2021 by Teachoo

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Sample Space When die is thrown 3 timesA die is thrown 3 times S = {(1, 1, 1), (1, 1, 2), ......, (1, 1, 6), (1, 2, 1), (1, 2, 2), ......, (1, 2, 6), (1, 3, 1), (1, 3, 2), ......, (1, 3, 6), (1, 4, 1), (1, 4, 2), ......, (1, 4, 6), (1, 5, 1), (1, 5, 2), ......, (1, 5, 6), (1, 6, 1), (1, 6, 2), ......, (1, 6, 6), (2, 1, 1), (2, 1, 2), ......, (2, 1, 6), (2, 2, 1), (2, 2, 2), ......, (2, 2, 6), (2, 3, 1), (2, 3, 2), ......, (2, 3, 6), (2, 4, 1), (2, 4, 2), ......, (2, 4, 6), (2, 5, 1), (2, 5, 2), ......, (2, 5, 6), (2, 6, 1), (2, 6, 2), ......, (2, 6, 6), (3, 1, 1), ......, (3, 1, 6), (3, 2, 1),......, (3, 2, 6), (3, 3, 1),......, (3, 3, 6), (3, 4, 1),......, (3, 4, 6), (3, 5, 1),......, (3, 5, 6), (3, 6, 1),......, (3, 6, 6), (4, 1, 1), ……………..(4, 6, 6), (5, 1, 1), ……………..(5, 6, 6), (6, 1, 1), ……………..(6, 6, 6)} Total number = 6 × 6 × 6 = 216 Ex 13.1, 8 A die is thrown three times, E : 4 appears on the third toss, F : 6 and 5 appears respectively on first two tosses Determine P(E|F) A die is thrown 3 times S = {(1, 1, 1) ,.........., (1, 6, 6), (2, 1, 1), .........., (2, 6, 6), (3, 1, 1), .........., (3, 6, 6), (4, 1, 1), ……………..(4, 6, 6), (5, 1, 1), ……………..(5, 6, 6), (6, 1, 1), ……………..(6, 6, 6), Total cases = 6 × 6 × 6 = 216 Given, E : 4 on the third throw F : 6 on the first & 5 on the second throw Thus, E ∩ F = {(6,5,4)} So, P(E ∩ F) = 1/216 Same as Example 5 E = { (1, 1, 4), (1, 2, 4), ……., (1, 6 ,4), (2, 1, 4), (2, 2, 4), ……., (2, 6, 4), (3, 1, 4), (3, 2, 4), ……., (3, 6, 4), (4, 1, 4), (4, 2, 4), ……., (4, 6, 4), (5, 1, 4), (5, 2, 4), ……., (5, 6, 4), (6, 1, 4), (6, 2, 4), ……., (6, 6, 4), } P(E) = 36/216 F = {(6, 5, 1), (6, 5, 2), (6, 5, 3), (6, 5, 4), (6, 5, 5), (6, 5, 6) } P(F) = 6/216 We need to find P(E|F) Now, P(E|F) = (𝑃(𝐸 ∩ 𝐹))/(𝑃(𝐹)) = (1/216)/(6/216) = 1/6 ∴ P(E|F) = 𝟏/𝟔 Same as Example 5

Ex 13.1

Ex 13.1, 1

Ex 13.1, 2

Ex 13.1, 3 Important

Ex 13.1, 4

Ex 13.1, 5

Ex 13.1, 6 (i)

Ex 13.1, 6 (ii) Important

Ex 13.1, 6 (iii)

Ex 13.1, 7 (i)

Ex 13.1, 7 (ii)

Ex 13.1, 8 You are here

Ex 13.1, 9

Ex 13.1, 10 (a) Important

Ex 13.1, 10 (b) Important

Ex 13.1, 11

Ex 13.1, 12 Important

Ex 13.1, 13 Important

Ex 13.1, 14

Ex 13.1, 15

Ex 13.1, 16 (MCQ) Important

Ex 13.1, 17 (MCQ) Important

Chapter 13 Class 12 Probability (Term 2)

Serial order wise

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.