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Sampling senators The two-way table describes the members of the U.S. Senate in a recent year. Suppose we select a senator at random. Consider events D: is a democrat, and F: is female.

(a) Find P(D | F). Explain what this value means.

(b) Find P(F | D). Explain what this value means.

Short Answer

Expert verified

Part (a)P (D|F) =0.7647

Part (b) P(F|D)=0.2167

Step by step solution

01

Part (a) Step 1. Given Information

The results are distributed as follows:

02

Part (a) Step 2. Concept Used

The number of favorable outcomes divided by the total number of possible outcomes equals probability. As a result, the following is a definition of condition probability: P(A|B)=P(AandB)P(B)

03

Part (a) Step 3. Calculation

The person in issue is female, according to the inquiry. Now we must determine the likelihood that the result for "democrats" will be positive.

Therefore,

P(DandF)=favorableoutcomespossibleoutcomes=1347+13+36+4=13100

P(F)=favorableoutcomespossibleoutcome13+4100=17100

As a result, the conditional probability is:

P(D|F)=P(DandF)P(F)=13170.7647

As a result, the likelihood of a favorable outcome for "democrats" is high.

P(D|F)=0.7647

04

Part (b) Step 1. Calculation

The person is a democrat, according to the question. Now we must determine the likelihood that the result for "female" is correct.

Therefore,

P(DandF)=favourableoutcomespossibleoutcomes=1347+13+36+4=13100

P(D)=favourableoutcomespossibleoutcomes=47+13100=60100

As a result, the conditional probability is:

P(F|D)=P(DandF)P(D)=13600.2167

As a result, the likelihood that the "female" result will be positive is high.

P(F|D)=0.2167

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