Slide20.JPG

Slide21.JPG
Slide22.JPG

Subscribe to our Youtube Channel - https://you.tube/teachoo

  1. Chapter 13 Class 12 Probability
  2. Serial order wise

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’’^(๐’โˆ’๐’™) ๐’‘^๐’™ Here, n = number of rounds fired p = Probability of hitting = 3/4 q = 1 โ€“ p = 1 โˆ’ 3/4 = 1/4 Hence, P(X = x) = nCx (๐Ÿ‘/๐Ÿ’)^๐’™ (๐Ÿ/๐Ÿ’)^(๐’โˆ’๐’™) 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 โ‰ฅ 1) > 99%, we need to find n Now, P(X โ‰ฅ 1) > 99 % 1 โˆ’ P(X = 0) > 99 % ` 1 โˆ’ nC0(3/4)^0 (1/4)^๐‘›> 0.99 1 โˆ’ (1/4)^๐‘› > 0.99 1 โˆ’ 0.99 > (1/4)^๐‘› 0.01 > 1/4^๐‘› 4^๐‘› > 1/0.01 ๐Ÿ’^๐’ > ๐Ÿ๐ŸŽ๐ŸŽ We know that 44 = 256 So, n โ‰ฅ 4 So, the minimum value of n is 4 So, he must fire atleast 4 times `

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
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.