Group of 2000 randomly selected adults were asked if they ar

Group of 2000 randomly selected adults were asked if they are in favor of or against closing. The following table gives the responses If one person is selected at random from these 2000 adults find the probability that this person is Are the events \"Female\" and \"no opinion\" Independent? Why or why not?

Solution

B.

Let

F = female
N = no opinion

Note that if they are independent, then

P(F) = P(F|N)

Herem

P(F) = (300+680+120)/2000 = 0.55
P(F|N) = 120/(120+100) = 0.545454545

Since they are not equal (although they are close!), then they are NOT independent. [ANSWER]

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