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

Question

asked Aug 11, 2019 33.2k views

1 Answer

Maximo Dominguez · Answer 1 · 2019-08-16T06:17:29+0000

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:

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