# Misc 7 - Chapter 13 Class 12 Probability

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 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) × 16 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 𝒒𝒏−𝒙 𝒑𝒙 Where n = number of times die is thrown = 5 p = Probability of getting a six = 16 q = 1 – 16 = 56 Hence, P(X = x) = 5Cx 𝟏𝟔𝒙 𝟓𝟔𝟓 − 𝒙 We need to find P(getting 2 sixes in 5 throws) i.e. P(X = 2) P(X = 2) = 5C2 162 565 − 2 = 5! 5 − 2 ! 2 ! 162 563 = 5 × 4 × 3 × ! 3 ! × 2 ! 16 × 6 × 56 = 10 62 563 = 10 × 5362 × 63= 10 × 53 65 Hence, Required Probability = P(X = 2) × 16 = 10 × 53 65 × 16 = 10 × 53 66 = 10 × 12546656 = 𝟔𝟐𝟓𝟐𝟑𝟑𝟐𝟖

Chapter 13 Class 12 Probability

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 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.