Subscribe to our Youtube Channel - https://www.youtube.com/channel/UCZBx269Tl5Os5NHlSbVX4Kg
Example 35 - Chapter 13 Class 12 Probability
Last updated at Feb. 15, 2020 by Teachoo
Transcript
Example 35 The probability of a shooter hitting a target is 3/4 . How many minimum number of times must he/she fire so that the probability of hitting the target at least once is more than 0.99?Let X : Number of times he hits the target Hitting the target is a Bernoulli trial So, X has a binomial distribution P(X = x) = nCx ๐^(๐โ๐) ๐^๐ Here, n = number of rounds fired p = Probability of hitting = 3/4 q = 1 โ p = 1 โ 3/4 = 1/4 Hence, P(X = x) = nCx (๐/๐)^๐ (๐/๐)^(๐โ๐) We need to find How many minimum number of times must he/she fire so that the probability of hitting the target at least once is more than 0.99 So, given P(X โฅ 1) > 99%, we need to find n Now, P(X โฅ 1) > 99 % 1 โ P(X = 0) > 99 % ` 1 โ nC0(3/4)^0 (1/4)^๐> 0.99 1 โ (1/4)^๐ > 0.99 1 โ 0.99 > (1/4)^๐ 0.01 > 1/4^๐ 4^๐ > 1/0.01 ๐^๐ > ๐๐๐ We know that 44 = 256 So, n โฅ 4 So, the minimum value of n is 4 So, he must fire atleast 4 times `
Examples
Example 1
Example 2
Example 3
Example 4
Example 5 Important
Example 6
Example 7 Important
Example 8
Example 9 Important
Example 10
Example 11 Important
Example 12 Important
Example 13 Important
Example 14 Important
Example 15 Important
Example 16
Example 17 Important
Example 18 Important
Example 19 Important
Example 20 Important
Example 21 Important
Example 22
Example 23
Example 24 Important
Example 25 Important
Example 26 Important
Example 27
Example 28 Important
Example 29 Important
Example 30 Important
Example 31 Important
Example 32 Important
Example 33 Important
Example 34 Important
Example 35 Important You are here
Example 36 Important
Example 37 Important
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.