Ex 13.2, 7 - Chapter 13 Class 12 Probability

Last updated at April 16, 2024 by

Ex 13.2, 7 - If P(A) = 1/2, P(AUB) = 3/5, P(B) = p. Find p

Ex 13.2, 7 - Chapter 13 Class 12 Probability - Part 2
Ex 13.2, 7 - Chapter 13 Class 12 Probability - Part 3
13.2, 7 (ii).jpg

Transcript

Ex 13.2, 7 (i) Given that the events A and B are such that P(A) = 1/2 , P (A ∪ B) = 3/5 and P(B) = p. Find p if they are (i) mutually exclusiveGiven, P(A) = 1/2 , P (A ∪ B) = 3/5 and P(B) = p. Since sets A & B are mutually exclusive, So, they have nothing in common ∴ P(A ∩ B) = 0 We know that P(A ∪ B) = P(A) + P(B) – P(A ∩ B) Putting values 3/5 = 1/2 + p – 0 3/5 – 1/2 = p (6 − 5)/10 = p 1/10 = p p = 𝟏/𝟏𝟎 Ex 13.2, 7 (ii) Given that the events A and B are such that P(A) = 1/2 , P (A ∪ B) = 3/5 and P(B) = p. Find p if they are (ii) independent.Since events A & B are independent, So, P(A ∩ B) = P(A) P(B) = 1/2 × p = 𝑝/2 Now, P(A ∪ B) = P(A) + P(B) – P(A ∩ B) Putting values 3/5 = 1/2 + p – 𝑝/2 3/2 – 1/2 = p – 𝑝/2 (6 − 5)/10 = 𝑝/2 1/10 = 𝑝/2 p = 2/10 p = 𝟏/𝟓

Go Ad-free
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 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.