Finite Math: Probability & Independence

Question

Last year in Way-up-there Alaska voted for mayor with the following results:

	Democrat	Republican	Bull-Moose Party
Male	12	22	21
Female	24	13	33

One of these voters is selected at random.

(a) What is the probability that this person voted Democrat?

(b) What is the probability that this person is a female who voted Democrat?

(c) If the person selected is female, what is the probability that this person voted Democrat?

(d) If the person selected voted Democrat, what is the probability that this person is female?

(e) Are the events “voted Democrat” and “female” independent? Why or why not?

Answer 1

Let's total the number of people for each category.

Democrats: 36 Male: 55

Republicans: 35 Female: 70

Bull-Moose Party: 54 Total: 125

Total: 125

a.) P(Democrat) = 36/125 = 0.288

The probability that the person is a Democrat is 0.288.

b.) P(Female and Democrat) = 24/125 = 0.192

The probability that the person is a female and a Democrat is 0.192.

c.) P(Democrat|Female) = 24/70 = 0.3429

The probability that this person is a Democrat given that the person is a female is 0.3429.

d.) P(Female|Democrat) = 24/36 = 0.6667

The probability that this person is a female given that the person is a Democrat is 0.6667.

e.) P(Female and Democrat) = P(Democrat)*P(Female|Democrat) = (0.288)(0.6667) = 0.192

This is the same as P(Female)*P(Democrat|Female) = (70/125)*(24/70) = 24/125 = 0.192.

Therefore, both events are independent.