In Carter County, 21% of the population lives in the county seat, while the rest
ID: 3294706 • Letter: I
Question
In Carter County, 21% of the population lives in the county seat, while the rest live in the countryside. Suppose 3% of those living in the county seat are selected for jury duty, while 3.5% of those living in the countryside are selected for jury duty. A resident of the county is randomly chosen. Let D be the event that the person is selected for jury duty, E1 be the event that the person is from the county seat, and E2 be the event that the person is from the countryside. Complete parts (a) through (c) below. a. Find the probability that this person is selected for jury duty Write an equation that models the probability. Choose the correct answer below The probability is (Round to three decimal places as needed.) b. Find the probability that this person is from the county seat, given that this person is selected for jury duty. Write an expression that models the probability. Choose the correct answer below P() . P(E1) P(DIE) .PE)+P(DE2) .P(E2) P (DIE2).PE) P (E2lD) .PD) P(ED) .PD)+P(E2DP(D) P(E, D) P(D) P(E,ID) P(D)E2D.PD) OA.Explanation / Answer
a. Probability that the random person of the person living in the country As D, E1 and E2 is defined in the question.
We can say the P(D) = P (D l E1) * P(E1) + P(D l E2) * P(E2) (OPtion B is correct)
P = 0.21 * 0.03 + 0.79 * 0.035 = 0.034
b. Here the condition is that persongot the jury duty, now we want to know is it from county seat.
As in the last question we have calculated the probability for a random person to get a coupon.
so Pr (Country Seat l Jury Duty ) = Pr (County seat and Jury Duty) / Pr( Jury Duty)
= P (D l E1) * P(E1) / [P (D l E1) * P(E1) + P(D l E2) * P(E2)]
Option A is correct.
so the probability is P1 = 0.21 * 0.03/ (0.21 * 0.03 + 0.79 * 0.035) = 0.186
(c) Here Person didn't received JUry Duty and we have to tell that it is from the Countryside
Pr ( Countrysidel Didn't received Jury duty) = Pr ( Countryside and Didn't received Jury duty) / Pr(Didn't received Jury Duty)
Pr(Didn't received JUry DUty ) = 1 - Pr ( Received the coupon) = 1- 0.034 = 0.966
Pr ( Countryside and Didn't received Jury duty) = 0.21 * (1 - 0.03) = 0.2037
so Pr ( South Tower l Didn't received the coupon) = 0.2037/ 0.966 = 0.211