Check sibling questions

Example 7 - If coin shows head, toss it again but if shows tail

Example 7 - Chapter 13 Class 12 Probability - Part 2
Example 7 - Chapter 13 Class 12 Probability - Part 3
Example 7 - Chapter 13 Class 12 Probability - Part 4

Solve all your doubts with Teachoo Black (new monthly pack available now!)


Transcript

Example 7 Consider the experiment of tossing a coin. If the coin shows head, toss it again but if it shows tail, then throw a die. Find the conditional probability of the event that ‘the die shows a number greater than 4’ given that ‘there is at least one tail’.A coin is tossed If the coin shows head, it is tossed again. If it shows tail, then a die is thrown. Hence different value of probabilities are We need to find the probability that the die shows a number greater than 4, given that there is at least one tail. Now, E : at least one tail F : Number greater than 4 on the die We need to find P(E|F) Also, E ∩ F = {(T, 5), (T, 6)} E = { (T, 5), (T, 6) } P(E) = P(T, 5), P(T, 6) = 1/12 + 1/12 = 2/12 = 1/6 F = { (H, T), (T, 1), (T, 2), (T, 3), (T, 4), (T, 5), (T, 6) } P(F) = P(H,T) + P(T,1) + P(T,2) + P(T,3) + P(T,4) + P(T,5) + P(T,6) = 1/4 + 1/12 + 1/12 +1/12 +1/12 +1/12 + 1/12 + 1/12 = 1/4 + 6/12 = 1/4 + 1/2 = 3/4 So, P(E ∩ F) = P(T, 5) + P(T, 6) = 1/12 + 1/12 = 2/12 = 1/6 Now, P(E|F) = (𝑃(𝐸 ∩ 𝐹))/(𝑃(𝐹)) = (1/6)/(3/4) = 1/6 × 4/3 = 𝟐/𝟗 Therefore, required probability is 2/9

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.