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IF P(A)=1/3, P(B)=2/5, and P(AuB)=3/5, what is P(A^B)?

1 Answer

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The probability of the union of two events is the sum of their probability, minus the probability of their interserction:


P(A \cup B) = P(A) + P(B) - P(A \cap B)

If we plug the known values into this formula, we have


(3)/(5) = (1)/(3) + (2)/(5) - P(A\cap B)

From which we can deduce


P(A\cap B) = (1)/(3) + (2)/(5) - (3)/(5) = (2)/(15)

So, the probability of
A \setminus B is a bit less than
P(A), we have to take away all events that belong to B as well:


P(A \setminus B) = P(A) - P(A\cap B) = (1)/(3) - (2)/(15) = (1)/(5)

User Maximo Dominguez
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