In a random experiment, let A and B be events such that P(A or B) = 0.

1.	In a random experiment, let A and B be events such that P(A or B) = 0.7, P(A and B) = 0.3 and P bar (A) = 0.4. Find P(B).
Answer» Given : \(P( \bar{A})\) = 0.4, P(A or B) = 0.7 and P(A and B) = 0.3 To find : P(B) Formula used : P(A) = 1 – \(P( \bar{A})\) P(A or B) = P(A) + P(B) - P(A and B) We have \(P( \bar{A})\) = 0.4 P(A) = 1 – 0.4 = 0.6 We get P(A) = 0.6 Substituting in the above formula we get, 0.7 = 0.6 + P(B) – 0.3 0.7 = 0.3 + P(B) 0.7 – 0.3 = P(B) 0.4 = P(B) P(B) = 0.4

In a random experiment, let A and B be events such that P(A or B) = 0.7, P(A and B) = 0.3 and P bar (A) = 0.4. Find P(B).

Answer»

Given : \(P( \bar{A})\) = 0.4, P(A or B) = 0.7 and P(A and B) = 0.3

To find : P(B)

Formula used : P(A) = 1 – \(P( \bar{A})\)

P(A or B) = P(A) + P(B) - P(A and B)

We have \(P( \bar{A})\) = 0.4

P(A) = 1 – 0.4 = 0.6

We get P(A) = 0.6

Substituting in the above formula we get,

0.7 = 0.6 + P(B) – 0.3

0.7 = 0.3 + P(B)

0.7 – 0.3 = P(B)

0.4 = P(B)

P(B) = 0.4

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In a random experiment, let A and B be events such that P(A or B) = 0.7, P(A and B) = 0.3 and P bar (A) = 0.4. Find P(B).

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