Question

(18 pts.) Below is a table of 200 adults who were asked to identify their political affiliation and whether they consider

themselves liberal, moderate or conservative. If one of these voters is selected at random for a follow-up interview,

Democrat Republican Independent

Liberal. 50 6 8

Moderate 26 18 14

Conservative 16 56 6

a. Find the probability that the voter selected is a Republican.

b. Find the probability that the voter selected is a Democrat and self-identifies as liberal.

c. Find the probability that the voter selected is a Democrat or self-identifies as liberal.

d. Find the probability that the voter selected is neither a Democrat nor self-identifies as liberal.

e. Find the probability that the voter selected is a Democrat, given that he/she is self-identifies as liberal.

f. Find the probability that the voter selected self-identifies as conservative, given that he/she is Republican.

Answer 1

	Democrat	Republican	Independent	Total
Liberal	50	6	8	64
Moderate	26	18	14	58
Conservative	16	56	6	78
Total	92	80	28	200

(a) The probability that the voter selected is a Republican = 80/200 = 0.4

(b) The required probability = 50/200 = 0.25

(c) (64 + 92 - 50)/200 = 0.53

(d) The required probability = 1 - P(Democrat or self identifies as liberal)

= 1 - 0.53 = 0.47

(e) The required probability = P(Democrat | self-identifies as liberal)

= 50/64 = 0.78125

(f) The required probability = P(self-identifies as conservative | Republican) = 56/80 = 0.70