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Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


Transcript

Ex 13.1, 11 A fair die is rolled. Consider events E = {1, 3, 5}, F = {2, 3} and G = {2, 3, 4, 5}. Find (i) P(E|F) and P (F|E)A fair die is rolled S = {1, 2, 3, 4, 5, 6} Event E E = {1, 3, 5} P(E) = 3/6 = 1/2 Event F F = {2, 3} P(F) = 2/6 = 1/3 Event G G = {2, 3, 4, 5} P(G) = 4/6 = 2/3 We need to find P(E|F) and P(F|E) Now, "E"∩"F" = {3} P("E"∩"F") = 1/6 Now, P(E|F) = (𝑃(𝐸 ∩ 𝐹))/(𝑃(𝐹)) = (1/6)/(1/3) = 𝟏/𝟐 P(F|E) = (𝑃(𝐹 ∩ 𝐸))/(𝑃(𝐸)) = (1/6)/(1/2) = 𝟏/𝟑 Ex 13.1, 11 A fair die is rolled. Consider events E = {1, 3, 5}, F = {2, 3} and G = {2, 3, 4, 5}. Find (iii) P((E ∪ F)|G) and P((E ∩ F)|G)P ( ("E"∪"F) | G ") Let "E"∪"F" = A So, A = {1, 2, 3, 5} P(A) = 4/6 Now, "A"∩"G" = {2, 3, 5} So, P("A"∩"G") = 3/6 Thus, P("A|G") = (𝑃(𝐴 ∩ 𝐺))/(𝑃(𝐺)) = (3/6)/(4/6) = 𝟑/𝟒 Therefore, P ( ("E"∪"F) | G ") = 𝟑/𝟒 Similarly, let’s do for P ( ("E"∩"F) | G" ) P( ("E"∩"F) | G ") Let "E"∩"F" = B So, B = {3} P("B") = 1/6 Now, "B"∩"G" = {3} So, P("B"∩"G") = 1/6 Thus, P("B|G") = (𝑃(𝐵 ∩ 𝐺))/(𝑃(𝐺)) = (1/6)/(4/6) = 𝟏/𝟒 Therefore, P ( ("E"∩ "F) | G ") = 𝟏/𝟒

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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.