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ID: 3305402 • Letter: Y
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YOUR NAME INSTRUCTIONS: PLEASE DO NOT WRITE ANYTHING ON THIS PAPER OTHER THAN YOUR NAME; IN SEPARATE SHEETS OF BLANK PAPER, SHOW YOUR WORK -IN SEQUENCE (1) FOLLOWED BY (2)..ETC (1) (16POINTS; 4 pts each) In a local population of voters 40% are Republicans,50% are Democrats and 10% are independents. An election issue is to be decided in a local election, t is known that 45% of the Republicans favor the issue; while 40% of the Democrats and 60% of the Independents respectively favor the issue. A voter is selected at random; (a)find the conditional probability that the selected voter a Democrat given that he/she favors the issue (b) Find the conditional probability that the selected voter is a Republican given that he/she does favor the issue ©. Find the conditional probability that the selected voter is an independent given that he/she does favor the issue (d)Given that the randomly selected voter favors the issue, what is the most probable a party affiliation of the voter? (2) (16 pts; 4 pts each) Two switches (1) and (2) are connected in series in a line that is connected in paralel to a third switch (3) as shown in the diagram below. These switches work independently when turned on and have the probabilities of working : P(l)-P(2)=8; (3) =.9 when the switches are turned on a) Find the probability that the current will flow thru the circuit b)Find the probability that no current will low thru the circuit © Find the probability that the current will flow thru both branches of the circuit. (d) Find the probability that the current will flow thru exactly one branch of the circut DIAGRAMExplanation / Answer
P(favor the issue) = P(republican favor the issue)+ P(democrat favor the issue) + P(independent favor the issue)
= 0.4 x 0.45 + 0.5x0.4 + 0.1x0.6
= 0.18 + 0.2 + 0.06
= 0.44
a) P(democrat | favor the issue) = P(democrat and favor the issue) / P(favor the issue)
= 0.2/0.44 = 0.4545
b) P(republican | favor the issue) = P(republican and favor the issue) / P(favor the issue)
= 0.18/0.44 = 0.4091
c) P(independent | favor the issue) = P(independent and favor the issue) / P(favor the issue)
= 0.06/0.44 = 0.1364
Given that a randomly selected person favors the issue, the most probable party affiliation is democrat.
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