Consider the following game of chance based on the spinner below: Each spin costs $2. If the spinner lands on?
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Consider the following game of chance based on the spinner below: Each spin costs $2. If the spinner lands on D the player wins a penny, if the spinner stops on A the player wins $8 otherwise the player wins nothing. Calculate the players expected winnings There is a 1/4 chance that the spinner will land on A and a 1/6 chance that the spinner will land on D
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Answer:
I came up with the same answer Rosinboi did. He is correct: .25 * 8 + (1 - (1/4 + 1/6)) * 0 + (1/6) * .01 ------------------ 2.001667 <------ expected return If the cost of each play is $2.00, you can see a profit is made each on each spin... a SMALL profit. .001667. <----- expected winnings
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Other answers
You question needs a little more detail. I am assuming there is also a "B" and "C" which will give no return. Also the expected winnings can only be calculated on a set number of spins. For example your question could be, what in accordance with probability will be the average earnings on 10 spins?
mike
It's a simple math problem. To calculate expected winnings you do the amount times the chance so, $8 times chance of A, $0 times chance of B, etc. That gives you: 8(1/4)+0.01(1/6)+0[1-(1/4+1/6)] = 2.00166667 aka 2+1/600. Since it costs $2 to play, your expected winnings is only $1/600
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