Question

1. Policy Pollsters [PP] is a market research firm specializing in political polls. Records indicate that in past elections, when a candidate was elected, Policy Pollsters had accurately predicted this 85% of the time and was wrong only 15% of the time. Records also show that, for losing candidates, Policy Pollsters accurately predicted that they lose 75% of the time and was wrong 25% of the time. Before the poll is conducted, there is a 50% chance of winning the election.

a. If a poll conducted by PP predicts a candidate will lose the election, what is the probability that the candidate will win the election? Show your work.        [2 points]

b. What is the probability that a poll conducted by PP predicts a candidate will win the election and the candidate loses the election? Show your work.                  [2 points]

c. Are the PP poll predicting a loss and the candidate losing the election independent events? Please show how you arrived at your answer.                                 [1 point]

Answer 1

P(PP pred Candidate 0.85 TAPP predicts candidate will win | Carti ----..actually wins.) - PLATW) - so, PC ALW) = 0.15 & PLACI WC) = 0.75 & PC Alwe) = 0.25 Before the poll is conducted there is a 50% chance of winning the election, so . _PCW) = P(W) = 0.5 az PC W LA) ... PCACI.n)PCW) P(A²) - PCACW) P(W) PCASIW) PCW) + PC ACIW9) P(WS) I Using Bayes theorum ] 0:15 0.15 x 0.5 x + 0.5 0.75 x 0.5 0.1667_ by e We A = P(AIWC) P(WC) PCA) PAIWC) P (WC) P(AIWC) P (WC) + P(AIW) P(W) 0-25 x 0.5 0:25*0.5 + 0.8.5 40.5 0.22728

Ac e. We have to conclude it events e we are independent events, - he already know. - Powe) = 0:5 We will find out P(WCTAC) PC WCIA). | PCWLAS) = I 0:1607 . : := 0.8333 Since !.P(krc) # P (W CIAC). were are can not conclude that we & Ac independent events