If E and F are independent events with P(E)=0.87 and P(F)=0.14 , find:
a. P (E/F)
b. P (F/E)
c. P ( E n F)
d. P ( E u F)
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a. P(E|F) = P(E and F)/P(F)
Since these are independent events, P(E and F) = P(E)P(F)
P(E|F) = (0.87)(0.14)/(0.14)
b. P(F|E) = P(F and E)/P)(E)
P(F|E) = P(0.14)(0.87)/(0.87)
c. P(E and F) = P(E)P(F)
P(E and F) = (0.14)(0.87)
d. P(E or F) = P(E) + P(F) - P(E and F)
(0.87) + (0.14) - (0.87)(0.14)
Note that the conditional probability of independent events is simply the product of those two events. The reason why this is true is because neither event depends upon each other, so the occurrence of one event does not affect the occurrence of another event. For example, if I use my cell phone, does that affect whether it is cloudy out that day? Or if it is cloudy out that day, does that affect the probability of me using my cell phone? No, because the events are completely independent of one another.