A and B are two events associated with random experiment for which P(A

1.	A and B are two events associated with random experiment for which P(A) = 0.36, P(A or B) = 0.90 and P(A and B) = 0.25. Find(i) P(B)(ii) P(\(\bar{A}\) ∩ \(\bar{B}\))
Answer» (i) Given P(A) = 0.36, P(A ∪ B) = 0.09, P(A ∩ B) = 0.25 P(A ∪ B) = P(A) + P(B) – P(A ∩ B) (i.e.,) 0.90 = 0.36 + P(B) – 0.25 0.90 = 0.11 + P(B) ∴ P(B) = 0.90 – 0.11 = 0.79 (ii) P(\(\bar{A}\) ∩ \(\bar{B}\)) = P{(A’ ∪ B)’} (Demorgan Law) P(A ∪ B)’ = 1 – P(A ∪ B) = 1 – 0.90 = 0.1

A and B are two events associated with random experiment for which P(A) = 0.36, P(A or B) = 0.90 and P(A and B) = 0.25. Find(i) P(B)(ii) P(\(\bar{A}\) ∩ \(\bar{B}\))

Answer»

(i) Given P(A) = 0.36, P(A ∪ B) = 0.09, P(A ∩ B) = 0.25

P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

(i.e.,) 0.90 = 0.36 + P(B) – 0.25

0.90 = 0.11 + P(B)

∴ P(B) = 0.90 – 0.11 = 0.79

(ii) P(\(\bar{A}\) ∩ \(\bar{B}\)) = P{(A’ ∪ B)’} (Demorgan Law)

P(A ∪ B)’ = 1 – P(A ∪ B) = 1 – 0.90 = 0.1

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A and B are two events associated with random experiment for which P(A) = 0.36, P(A or B) = 0.90 and P(A and B) = 0.25. Find(i) P(B)(ii) P(\(\bar{A}\) ∩ \(\bar{B}\))

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