Probability and Expected Value Concepts

This video tutorial explains the concept of expected value, which is the average gain or loss of an event if repeated many times. It demonstrates how to calculate expected value using two examples: a marble game and a warranty sales scenario. The tutorial covers the probability of different outcomes and how to compute the expected value by multiplying each outcome by its probability and summing the results. The video also highlights common mistakes in such calculations.

What is the expected value in probability theory?

• The most likely outcome of an event

• The average gain or loss of an event over many trials

• The sum of all possible outcomes

• The probability of the most frequent outcome

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CCSS.7.SP.C.7B

In the marble game, what is the probability of drawing a gold marble?

• 2/35

• 25/35

• 8/35

• 1/35

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CCSS.HSS.MD.B.5A

If you draw a silver marble, how much do you win in the marble game?

• $2

• $3

• $4

• $1

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CCSS.HSS.MD.B.5A

What is the expected value of the marble game?

• -$0.03

• $0.03

• $0.00

• -$0.01

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What is the probability that a product will fail after the warranty period in the second example?

• 0.009

• 0.09

• 0.9

• 0.99

How much does the company charge for a two-year extended warranty?

• $40.00

• $20.00

• $24.00

• $30.00

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CCSS.HSS.MD.A.2

What is the expected value for the company per warranty sold?

• $0.00

• $24.00

• $400.00

• $20.40

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CCSS.HSS.MD.B.6

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In the warranty example, what is the outcome for the company if the product fails?

• They lose $400

• They gain $24

• They gain $400

• They lose $376

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What is the probability that a product does not fail in the warranty example?

• 0.099

• 0.991

• 0.9

• 0.009

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CCSS.HSS.MD.B.5B

Why is it important to consider the warranty purchase in the failure outcome?

• It increases the failure probability

• It offsets the replacement cost by $24

• It has no impact on the expected value

• It reduces the replacement cost

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CCSS.HSS.MD.B.5B