Question

In a city, 60 % are conservatives, 14 % are liberals and 26 % are independents. Records show that, in a particular election, 70 % of conservatives voted, 76 % of liberals voted and 89 % of independents voted. For each of the following questions, express any probability value as a fraction or a decimal with 10 places.

If a person from such a city is selected at random and it is learned that he/she voted, what is the probability that he/she is liberal?
Answer:

If a person from such a city is selected at random and it is learned that he/she voted, what is the probability that he/she is independent?
Answer:

Answer 1

P(A /B) = P(A B) / P(B)

(a)

P( person is liberal / has voted) = P( person is liberal and has voted) / P(voted)

P (voted) = (0.60 * 0.70) + (0.14 * 0.76) + (0.26 * 0.89) = 0.7578

P(person is liberal and voted) = 0.14 * 0.76 =   0.1064

P( person is liberal / has voted) = 0.1064 / 0.7578 = 0.1404

ANS: P( person is liberal / has voted) = 0.1404

(b)

P( person is independent / has voted) = P( person is independent and has voted) / P(voted)

P (voted) = (0.60 * 0.70) + (0.14 * 0.76) + (0.26 * 0.89) = 0.7578

P(person is independent and voted) = (0.26 * 0.89) = 0.2314

P( person is lndependent/ has voted) = 0.2314 / 0.7578 = 0.3054

ANS: P( person is Independent / has voted) = 0.3054