Question 71537
1. Forty percent of the sales at a large insurance company have laptop computers, 65% have desktop computers and 24% have both. What percent of the sales people have either laptop or desktop computers?
P(lap or desk) = P(lap) + P(desk) - P(lap and desk)
=0.40+0.65-0.24=0.81
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2. Twenty percent of ABC Company’s employees are in Management. If an employee is in Management, there is a probability of 0.88 that he/she is a participant in the company’s stock purchase plan. Find the probability that an employee of this company is in Management and participates in the stock purchase plan.

P(Man and stock) = P(Man)*P(stock|Man)
=0.20*0.88 = 0.176
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3. Two cards are drawn in succession from a deck without replacement. What is the probability that both cards are red? 
These are dependent events because the card was not replaced.
P(red and red) = P(red)*P(red|red) = 26/52*25/51 = 0.245
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If the first card will be returned, what is the probability that first card is an ace and the second is a face card?
These are independent events because the card was replaced.
P(ace and face) = P(ace)*P(face)=(4/52)(12/52=48/2704=0.018
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4. In a certain university, 60% of all sophomores are enrolled in a Mathematics course, 73% are enrolled in an English course, and 49% are taking both. A student is randomly selected from this university.

a. What is the probability that the student is taking an English course, if it is known that he/she is enrolled in a Mathematics course?
These are conditional events.
P(eng | math) = P(eng and math)/P(math) =0.49/0.60=0.82
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b. If the student is taking an English course, what is the probability that he/she is also enrolled in a Mathematics course?
These are conditional events.
P(math | eng) = P(math and eng)/P(eng) = 0.49/0.73=0.67
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Cheers,
Stan