If PE intersection F 012 EF 021 and PFE 03 then PE PE U F

If P(E intersection F) = 0.12, (E|F) = 0.21, and P(F|E) = 0.3, then P(E) P(E U F) Are E and F independent? Why?

Solution

a)

As

P(E) = P(E and F) / P(F|E)

Then

P(E) = 0.12 / 0.3

= 0.4 [ANSWER]

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B)

As

P(F) = P(E and F) / P(E | F)

= 0.12 / 0.21

= 0.571428571

And

P(E U F) =P(E) +P(F) - P(E and F)

= 0.4 + 0.571428571 - 0.12

= 0.851428571 [ANSWER]

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c)

As P(E|F) =/ P(F|E), then no, they are no independent.