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alexandr402 [8]
3 years ago
5

Please helpppp it has to do with P(A U B)

Mathematics
1 answer:
Katyanochek1 [597]3 years ago
7 0
P(A)=0.5, P(B)=0.6, P(A\cup B)=0.8

We find the probability of intersection using the inclusion/exclusion principle:


P(A\cap B)=P(A)+P(B)-P(A\cup B)=0.3


By definition of conditional probability,


P(A\mid B)=\dfrac{P(A\cap B)}{P(B)}=\dfrac{0.3}{0.6}=0.5


For A and B to be independent, we must have


P(A\cap B)=P(A)\cdot P(B)

in which case we have 0.3=0.5\cdot0.6, which is true, so A and B are indeed independent.


Or, to establish independence another way, in terms of conditional probability, we must have

P(A\mid B)\cdot P(B)=P(A)\cdot P(B)\implies P(A\mid B)=P(A)


which is also true.
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