1.

For two events A and B in the sample space of a random experiment, P (A) = 2P(B’) = 3P (A ∩ B) = 0.6. Find the probability of difference events A – B and B – A.

Answer»

P(A’) = 2P(B’) = 3P(A ∩ B) = 0.6

∴ P(A’) = 0.6,
2P(B’) = 0.6 .
3P(A ∴ B) = 0.6

∴ P(B’) = \(\frac{0.6}{2}\) = 0.3
P(A ∩ B) =\( \frac{0.6}{3}\) = 0.2

P(A – B) = P(A ∩ B’)
= P(A) – P(A ∩ B)
= [1 -P(A’)] – P(A ∩ B)
= [1 – 0.6] – 0.2
= 0.4 – 0.2
= 0.2

P(B – A) = P(A’ ∩ B)
= P(B) – P(A ∩ B)
= [1 – P(B’)] – P(A ∩ B)
= [1 – 0.3] – 0.2
= 0.7 – 0.2
= 0.5


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