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. Note: Here we use combination as order of numbers is not important So, n(S) = 38760 To win a prize, there is only 1 case when six numbers match Let A be the event of winning lottery So, n(A) = 1 Probability of winning lottery P(A) = (𝑛(𝐴))/(𝑛(𝑆)) = 𝟏/𝟑𝟖𝟕𝟔𝟎

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.

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