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?
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.
3. Two cards are drawn in succession from a deck without replacement. What is the probability that both cards are red? If the first card will be returned, what is the probability that first card is an ace and the second is a face card?
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?
b. If the student is taking an English course, what is the probability that he/she is also enrolled in a Mathematics course?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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
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