Ex 13.3, 10 - Chapter 13 Class 12 Probability (Term 2)
Last updated at Feb. 15, 2020 by Teachoo
Bayes theorem
Ex 13.3, 2 Important
Ex 13.3, 3
Misc 3
Ex 13.3, 4 Important
Ex 13.3, 9
Ex 13.3, 5
Ex 13.3, 13 (MCQ) Important
Example 21 Important
Ex 13.3, 6 Important
Ex 13.3, 10 Important You are here
Example 18 Important
Example 17 Important
Ex 13.3, 7
Ex 13.3, 8 Important
Example 19 Important
Ex 13.3, 11
Ex 13.3, 12 Important
Example 37 Important
Example 20 Important
Example 33 Important
Misc 12
Misc 16 Important
Misc 13 Important
Bayes theorem
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) = (π(π΄) ." " π(πΆ|π΄))/(π(π΄) . π(πΆ|π΄) + π(π΅) . π(πΆ|π΅) ) "P(A)" = Probability that 1, 2, 3 or 4 appear on the die = 4/6 = π/π "P(C|A)" = Probability that exactly one head is obtained, if 1, 2, 3 or 4 appear on the die = π/π "P(B)" = Probability that 5 or 6 appear on the die = 2/6 = π/π "P(C|B)" = Probability that exactly one head is obtained, if 5 or 6 appear on the die = π/π Puttinag values in formula, P(A"|"C) = (2/3 Γ 1/2)/( 2/3 Γ 1/2 + 1/3 Γ 3/8 ) = (1/3 Γ 1/2 Γ 2)/( 1/3 Γ 1/2 [2 + 3/4 ] ) = 2/( 2 + 3/4 ) = 2/(11/4) = π/ππ Therefore, required probability is 8/11