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Last updated at Feb. 15, 2020 by Teachoo

Transcript

Misc 7 A die is thrown again and again until three sixes are obtained. Find the probability of obtaining the third six in the sixth throw of the die. We need to find probability of obtaining the third six in the sixth throw of the die. P(getting 3rd six in 6th throw) = P(getting 2 sixes in 5 throws) × P(getting a six on 6th throw) = P(getting 2 sixes in 5 throws) × 1/6 Calculating P(getting 2 sixes in 5 throws) Let X : be the number six we get on 5 throws Throwing a pair of die is a Bernoulli trial So, X has binomial distribution P(X = x) = nCx 𝒒^(𝒏−𝒙) 𝒑^𝒙 Here n = number of times die is thrown = 5 p = Probability of getting a six = 1/6 q = 1 – 1/6 = 5/6 Hence, P(X = x) = 5Cx (𝟏/𝟔)^𝒙 (𝟓/𝟔)^(𝟓 − 𝒙) We need to find P(getting 2 sixes in 5 throws) i.e. P(X = 2) P(X = 2) = 5C2 (1/6)^2 (5/6)^(5 − 2 ) = 5!/( (5 − 2) ! 2 !) (1/6)^2 (5/6)^3 = (5 × 4 × 3! )/(3 ! × 2 !) 1/(6 × 6) × (5/6)^3 = 10/(6^2 ) (5/6)^3 = (10 ×〖 5〗^3)/(6^2 × 6^3 ) =(10 ×〖 5〗^3)/6^5 Hence, Required Probability = P(X = 2) × 1/6 = (10 ×〖 5〗^3)/6^5 ×1/6 = (10 ×〖 5〗^3)/6^6 = (10 × 125)/46656 = 𝟔𝟐𝟓/𝟐𝟑𝟑𝟐𝟖

Miscellaneous

Misc 1

Misc 2 Important

Misc 3

Misc 4 Not in Syllabus - CBSE Exams 2021

Misc 5 Important Not in Syllabus - CBSE Exams 2021

Misc 6 Important Not in Syllabus - CBSE Exams 2021

Misc 7 Important You are here

Misc 8 Important

Misc 9 Important Not in Syllabus - CBSE Exams 2021

Misc 10 Important

Misc 11 Important

Misc 12

Misc 13 Important

Misc 14 Important

Misc 15 Important

Misc 16 Important

Misc 17 Important

Misc 18

Misc 19

Chapter 13 Class 12 Probability

Serial order wise

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.