# Ex 13.3, 10 - Chapter 13 Class 12 Probability

Last updated at April 16, 2024 by Teachoo

Chapter 13 Class 12 Probability

Serial order wise

Last updated at April 16, 2024 by Teachoo

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 = (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