Check sibling questions

Ex 13.5, 7 - In an examination, 20 questions of true-false

Ex 13.5, 7 - Chapter 13 Class 12 Probability - Part 2
Ex 13.5, 7 - Chapter 13 Class 12 Probability - Part 3

Learn Intergation from Davneet Sir - Live lectures starting soon!


Transcript

Ex 13.5, 7 In an examination, 20 questions of true-false type are asked. Suppose a student tosses a fair coin to determine his answer to each question. If the coin falls heads, he answers 'true'; if it falls tails, he answers 'false'. Find the probability that he answers at least 12 questions correctly.Let X : be the number of questions he answers correctly Tossing a coin is a Bernoulli trial So, X has binomial distribution P(X = x) = nCx 𝒒^(π’βˆ’π’™) 𝒑^𝒙 Here, n = number of questions = 20 p = Probability of getting answer correct Since it is a true false question P(he answers correctly) = p = 1/2 Thus, q = 1 – p = 1 – 1/2 = 1/2 Hence, P(X = x) = 20Cx (1/2)^π‘₯ (1/2)^(20βˆ’π‘₯) P(X = x) = 20Cx (1/2)^(20 βˆ’ π‘₯ + π‘₯) P(X = x) = 20Cx (𝟏/𝟐)^𝟐𝟎 We need to find probability that he answers at least 12 questions correctly i.e. P(X β‰₯ 12) P(X β‰₯ 12) = P(12) + P(13) + P(14) + …… ….. +P(20) = 20C12 (1/2)^20 + 20C13 (1/2)^20+ 20C14 (1/2)^20+ …… + 20C20 (1/2)^20 = (𝟏/𝟐)^𝟐𝟎(20C12 + 20C13 + 20C14 + …….. + 20C20)

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.