To test a new car. an automobile manufacturer wants to select 4 employees to tes

Question

To test a new car. an automobile manufacturer wants to select 4 employees to test drive the car for 1 year. If 12 management and 8 union employees volunteer to be test drivers and the selection is made at random, what is the probability that at least 1 union employee is selected? If a state resident is selected at random, what is the (empirical) probability that the resident is Not affiliated with a political1 party or has no preference? What are the odds for this event? Affiliated with a political party and prefers candidate A? What are the odds against this event? If a state resident is selected at random, what is the (empirical) probability that the resident is A Democrat or prefers candidate B? What are the odds for this event? Not a Democrat and has no preference? What are the odds against this event? to Matched Problems

Explanation / Answer

(A)

From table we have following probabilties:

P(D) = 500 / 1000

P(prefers candiadte B) = 530 / 1000

P(D and prefers candidate B) = 250 / 1000

So the probability that resident is a democrat oe prefers candidate B shows

P(D or prefer candidate B)= P(D) + P(prefers candidate B) - P(D and prefer candidate B) = (500/1000) + (530/1000) - (250/1000) = 780/1000

And the probability of complement of above event is

P[ not(D or prefer candidate B)] = 1- P(D or prefer candidate B) = 1- (780/1000) = 220 / 1000

So odds will be

odds = P(D and prefers candidate B) / P[ not(D or prefer candidate B)] = (780/1000) / (220 /1000) = 780 : 220 = 39 : 11

(B)

P(not a democrat and has no preference) = (20+15) / 1000 = 35 / 1000

And the probability of complement of above event is

P[ not(not a democrat and has no preference)] = 1- P(not a democrat and has no preference) = 1- (35/1000) = 965 / 1000

So odds will be

odds = P(not a democrat and has no preference) / P[ not(not a democrat and has no preference)] = (35/1000) / (965/1000) = 35 : 965 = 7 : 193

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