Math 451 Unit 4 Interactive Example
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Colorado Technical University *
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451
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Mathematics
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Feb 20, 2024
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Math 451
Unit 4 Estimating Probability Values
Interactive Examples
Question 1
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
$1.15
$1.00
$0.90
Solution
The correct answer is
$1.50
Correct
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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 2
What is the probability of having a negative response (NS)?
P(PS) = 0
P(PS) = 52.90%
P(NS) = 0.4710
P(PS) = 1
Solution
The correct answer is:
P(NS) = 0.4710
Correct
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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 at random out of his pocket and offers you a bet where he gets $1 if the heads side appears. 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.
Hint: You can use =BINOM.DIST() in Excel to compute the probabilities of the coin flips.
97%
75%
96%
88%
Solution
The correct answer is
96%
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 revised probability of having the high demand (HD) for a negative response (NS)?
P(HD|NS) = 0.3715
P(HD|NS) = 16%
P(HD|NS) = 0.5945
P(HD|NS) = 0.119
Solution
The correct answer is:
P(HD|NS) = 0.119
Wrong
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Question 5
You work for the spy agency CONTROL, and their arch enemy is KAOS, which is incorporated in Delaware for tax reasons. Recruiting agents is hard because not many people are qualified. Only about 1 in 397 people are qualified. There is a screening test. About 95% of the time, a qualified individual will pass the test, and about 3% of the time, an unqualified individual will get lucky and also pass the test. If a random person is chosen to take the test and he or she passes, what is the probability that the person is qualified? Round your answer off to the nearest tenth of a percent.
10.8%
7.4%
93.7%
10.4%
Solution
The correct answer is
7.4%
Correct
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