Question

[show your work. No need to simplify answer to a numeric value] The issue of corporate tax reform has been cause for much debate in the United States. Among those in the legislature, 29% are Republicans, 67% are Democrats and 4% are Independents. It is reported that 27% of the Republicans, 57% of the Democrats and 16% of Independents favor some type of corporate tax reform. In each of the problems, use the following letters and set theoretic notation to express each event. Then compute the probabilities. R = Being a republican, D = Being a democrat, I = Being an independent, F= In favor some type of corporate tax re [4 points] Suppose a member of Congress is randomly selected. What is the probability that he/she is in favor of some type of corporate tax reform? [4 points] Suppose a member of Congress is randomly selected and it is found that he/she is in favor of some type of corporate tax reform. What is the probability that this person is a Democrat? (democrate)×(F|D)/(Republican)×(favor │Republican)+(Democrat)×(f│D)+(independant)×(F│I) ((0.67)×(0.57))/((0.29)×(0.27)+(0.67)×(0.57)+(0.04)×(0.16)) [3 points] Suppose that a member of congress is selected at random. What is the probability that this member is a democrat and in favor of some type of corporate tax reform or an independent and in favor of some type of corporate tax reform? [2 points] Suppose that a member of congress is selected at random. What is the probability that this member is not in favor of some type of corporate tax reform?

Answer 1

Probability that the person is a Democrat given that he/she is in favor of some type of corporate tax reform, P(D|F)

= P(F|D) * P(D)/P(F)

where P(F) = P(F|D)*P(D) + P(F|R)*P(R) + P(F| I)* P(I)

= 0.27*0.29 + 0.57*0.67 + 0.16*0.04

= 0.4666

P(D|F) = 0.27*0.29/0.4666 = 0.1678

Probability that a randomly selected member is a Democrat and in favour of some type of corporate tax reform or an independent and in favor of some type of corporate tax reform

= P(D and F) + P(I and F)

= P(F|D)*P(D) + P(F| I)*P(I)

= 0.27*0.29 + 0.16*0.04 = 0.0847

Probability that a randomly selected member is not in favor of some type of corporate tax reform

= P(F') = 1 - P(F)

P(F) = 0.4666 is calculated above