Check sibling questions

Ex 16.3, 12 - Chapter 16 Class 11 Probability - Part 2

Ex 16.3, 12 - Chapter 16 Class 11 Probability - Part 3

 

This video is only available for Teachoo black users

Introducing your new favourite teacher - Teachoo Black, at only ₹83 per month


Transcript

Ex 16.3, 12 Check whether the following probabilities P(A) and P(B) are consistently defined P(A) = 0.5, P(B) = 0.7, P(A ∩ B) = 0.6 P(A) & P(B) are consistently defined if P(A ∩ B) < P(A) & P(A ∩ B) < P(B) P(A ∪ B) > P(A) & P(A ∪ B) > P(B) Given P(A) = 0.5, P(B) = 0.7, P(A ∩ B) = 0.6 Here, P(A ∩ B) > P(A). Hence, P(A) and P(B) are not consistently defined. Ex 16.3, 12 Check whether the following probabilities P(A) and P(B) are consistently defined (ii) P(A) = 0.5, P(B) = 0.4, P(A ∪ B) = 0.8 P(A) & P(B) are consistently defined if P(A ∩ B) < P(A) & P(A ∩ B) < P(B) P(A ∪ B) > P(A) & P(A ∪ B) > P(B) Given P(A) = 0.5, P(B) = 0.4 P(A ∪ B) = 0.8 Here, P(A ∪ B) > P(A) & P(A ∪ B) > P(B) Finding P(A ∩ B) We know that P(A ∪ B) = P(A) + P(B) – P(A ∩ B) Putting values 0.8 = 0.5 + 0.4 – P(A ∩ B) 0.8 = 0.9 – P(A ∩ B) P(A ∩ B) = 0.9 – 0.8 P(A ∩ B) = 0.1 So, P(A ∩ B) < P(A) & P(A ∩ B) < P(B) Since both conditions are satisfied, Hence, P(A) and P(B) are consistently defined.

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.