Question

In a city, 57 % are conservatives, 12 % are liberals and 31 % are independents. Records show that, in a particular election, 72 % of conservatives voted, 61 % of liberals voted and 80 % 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( Conservative) = 0.57

P( Liberals) = 0.12

P( Independent) =0.31

P( Voted | Conservative) = 0.72

P( Voted | Liberals) = 0.61

P(Voted | Independent) = 0.8

Thus, P (Voted)

= P( Voted | Conservative) * P( Conservative) + P( Voted | Liberals) * P( Liberals) + P(Voted | Independent)*P( Independent)

= 0.72 *0.57 + 0.61 * 0.12 + 0.8 * 0.31

=0.7316

a) P( Liberal | Voted ) =   P( Voted | Liberals) * P( Liberals) / P( Voted)

= (0.61 * 0.12) / 0.7316

= 183/1829

b) P( Independent | Voted) =P(Voted | Independent)*P( Independent) / P( Voted)

= (0.8 * 0.31 ) / 0.7316

=20/59