Chapter 13 Class 12 Probability

Class 12
Important Questions for exams Class 12

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### Transcript

Ex 13.3, 10 Suppose a girl throws a die. If she gets a 5 or 6, she tosses a coin three times and notes the number of heads. If she gets 1, 2, 3 or 4, she tosses a coin once and notes whether a head or tail is obtained. If she obtained exactly one head, what is the probability that she threw 1, 2, 3 or 4 with the die?Let A : 1, 2, 3, 4 appear on the die B : 5, 6 appear on the die C : exactly one head is obtained We need to find the Probability that if exactly one head is obtained on the toss of a coin, she threw 1, 2, 3 or 4 with the die i.e. P(A|C) P(A|C) = (𝑃(𝐴) ." " 𝑃(𝐶|𝐴))/(𝑃(𝐴) . 𝑃(𝐶|𝐴) + 𝑃(𝐵) . 𝑃(𝐶|𝐵) ) "P(A)" = Probability that 1, 2, 3 or 4 appear on the die = 4/6 = 𝟐/𝟑 "P(C|A)" = Probability that exactly one head is obtained, if 1, 2, 3 or 4 appear on the die = 𝟏/𝟐 "P(B)" = Probability that 5 or 6 appear on the die = 2/6 = 𝟏/𝟑 "P(C|B)" = Probability that exactly one head is obtained, if 5 or 6 appear on the die = 𝟑/𝟖 Puttinag values in formula, P(A"|"C) = (2/3 × 1/2)/( 2/3 × 1/2 + 1/3 × 3/8 ) = (1/3 × 1/2 × 2)/( 1/3 × 1/2 [2 + 3/4 ] ) = 2/( 2 + 3/4 ) = 2/(11/4) = 𝟖/𝟏𝟏 Therefore, required probability is 8/11

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#### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.