If PEF0072 PEF012 and PFE02 then a PE b PF c PEF d Are the e

If P(EF)=0.072, P(E|F)=0.12, and P(F|E)=0.2, then
(a)   P(E)=
(b)   P(F)=
(c)   P(EF)=
(d) Are the events E and F independent?  Enter yes or no .

Solution

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

So P(E) = P(E and F) / P(F|E) = 0.072 / 0.2 = 0.36

P(E) = 0.36

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

So P(F) = P(E and F) / P(E|F) = 0.072 / 0.12 = 0.6

P(F) = 0.6

c. P(E U F) = P(E) + P(F) - P(E and F) = 0.36 + 0.6 - 0.072 = 0.888

d. E and F are independent if and only if

P(E and F) = P(E) * P(F)

Now, P(E) * P(F) = 0.36*0.6 = 0.216

P(E and F) = 0.072 which is not equal to 0.216

So answer: No, they are not independent