An election forecasting model has a 50: 50 chance of correctly predicting the election winner when there are two candidates. before seeing the prediction of the model an election researcher estimates that there is a 75% chance that candidate allan will defeat candidate barnes. she then finds out that the model has predicted a victory for barnes. her posterior probability of a victory for allan should be: (a) (b) (c) (d) 0.375 0.500 0.750 1.000

Te correct answer is c) 0.750

Step-by-step explanation:

Lets call:

A = {Allan wins the election}

B = {Barnes wins the election}

MA = {the model predicts that Allan wins}

MB = {the model predicts Barnes wins}

We know that the model has a 50:50 chance of correctly predicting the election winner when there are two candidates. Then:

P(MA | A) = 0.5 = P(MA | B)

P(MB | B) = 0.5 = P(MB | A)

The prior probability P(A) given by the election researcher is 0.75

We must find the posterior probability P(A | MB)

We use Bayes theorem:

We used the result:

step-by-step explanation: