SOLUTION: Having problems understanding Random Variable, Probability Distribution and Expected Value. Please help. Question 1. The annual premium for a $5000 insurance policy against the

Question 451067: Having problems understanding Random Variable, Probability Distribution and Expected Value. Please help.
Question 1. The annual premium for a $5000 insurance policy against the theft of a painting is $150. If the (empirical) probability that the painting will be stolen during the year is.01, what is your expected return from the insurance company if you take out this insurance?
Question 2. On three rolls of a single die, you will lose $10 if a 5 turns up at least once, and you will win $7 otherwise. What is the expected value of the game?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Question 1. The annual premium for a $5000 insurance policy against the theft of a painting is $150. If the (empirical) probability that the painting will be stolen during the year is.01, what is your expected return from the insurance company if you take out this insurance?
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Random "return to you" values: 4850, -150
Corresponding Probabilities::: 0.01 , 0.99
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Expected "return to you" = 0.01*4850 + 0.99*(-150) = -$100.00
You can expect to lose $100 each year you have the policy.
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Question 2. On three rolls of a single die, you will lose $10 if a 5 turns up at least once, and you will win $7 otherwise. What is the expected value of the game?
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P(at least one 5 in three rolls) = 1 - P(no 5 in three) = 1-(5/6)^3 = 0.4213
P(other results) = 1-0.4213 = 0.5787
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Random game values: -10 , +7
Probabilities: 0.4213 , 0.5787
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Expected game value: 0.4213*(-10)+0.5787*7 = -0.16 = -16 cents
You can except to lose 16 cents each time you play the game.
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Cheers,
Stan H.
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