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(A or B) = 0.7, P(A and B) = 0.3 and P(bar A) = 0.4 We know, P(A) = 1 – P(bar A) = 1 – 0.4 = 0.6 So, P(A) = 0.6 Again, P(A or B) = P(A) + P(B) – P(A and B) By substituting values 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) Or 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(A or B) = 0.7, P(A and B) = 0.3 and P(bar A) = 0.4

We know, P(A) = 1 – P(bar A)

= 1 – 0.4 = 0.6

So, P(A) = 0.6

Again, P(A or B) = P(A) + P(B) – P(A and B)

By substituting values 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)

Or 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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