Question

The issue of corporate tax reform has been cause for much debate in the United States. Among those in the legislature, 27% are Republicans, 56% are Democrats and 17% are Independents. It is reported that 34% of the Republicans, 41% of the Democrats and 25% of Independents favor some type of corporate tax reform. Suppose a member of Congress is randomly selected and he/she is found to favor some type of corporate tax reform. What is the probability that this person is a Democrat?

Answer 1

Answer:

The probability Democrat is selected given that this member favors some type of corporate tax reform is 0.6309.

Step-by-step explanation:

Let us suppose that,

R = Republicans

D = Democrats

I = Independents.

X = a member favors some type of corporate tax reform.

The information provided is:

P (R) = 0.27

P (D) = 0.56

P (I) = 0.17

P (X|R) = 0.34

P (X|D) = 0.41

P (X|I) = 0.25.

Compute the probability that a randomly selected member favors some type of corporate tax reform as follows:

$P(X)=P(X|R)P(R)+P(X|D)P(D)+P(X|I)P(I)\\= (0.34\times0.27)+(0.41\times0.56)+(0.25\times0.17)\\=0.3639$

The probability that a randomly selected member favors some type of corporate tax reform is P (X) = 0.3639.

Compute the probability Democrat is selected given that this member favors some type of corporate tax reform as follows:

$P(D|X)=\frac{P(X|D)P(D)}{P(X)} =\frac{0.41\times0.56}{0.3639}=0.6309$

Thus, the probability Democrat is selected given that this member favors some type of corporate tax reform is 0.6309.