Math451 Unit 4 Interactive Examples

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Mathematics

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Feb 20, 2024

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Math 451 Unit 4 Interactive Examples A company is considering using a survey company that offers some sample information which may not be very accurate for better decision making for a value of $3,000 in this example. They have provided the following data for all alternatives that are consider here. Question 1 What is the probability of having a positive response (PS) for the high demand (HD)? P(PS|HD) = 0.125 P(PS|HD) = 84% P(PS|HD) = 0.60 P(PS|HD) = 16% Solution The correct answer is: P(PS|HD) = 84% Correct Hide solution Question 2 Suppose that your friend has a loaded coin that comes up heads 70% of the time and another coin that looks just like the weighted one but is fair. Your friend pulls a coin at random out of his pocket and offers you a bet where he gets $1 if the heads side appears. How much must you get for a tail for this bet to be fair? $1.50 $0.90 $1.25 $1.00 Solution The correct answer is $1.50 Correct Hide solution

Question 3 Suppose that your friend has a loaded coin that comes up heads 80% of the time and another coin that looks just like the weighted one but is fair. Your friend pulls a coin out of his pocket and offers you a bet where he gets $1 if the heads side appears. Your estimate of the probability that he has pulled the loaded coin is 90%. You are a bit uncomfortable with this, and insist on testing the coin. You flip it 5 times, and the heads side comes up once. Given this new information, how likely is it that you have the fair coin? Express your answer as a percentage rounded off to the nearest whole number. Hint: You can use =BINOM.DIST() in Excel to compute the probabilities of the coin flips. 61% 76% 73% 95% Solution The correct answer is 73% Correct Hide solution A company is considering using a survey company that offers some sample information which may not be very accurate for better decision making for a value of $3,000 in this example. They have provided the following data for all alternatives that are consider here. Question 4 What is the probability of having a positive response (PS) for the low demand (LD)? P(PS|LD) = 0.60 P(PS|LD) = 87.5% P(PS|LD) = 0.84 P(PS|LD) = 12.5% Solution The correct answer is: P(PS|LD) = 12.5% Correct

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