A game show contestant is offered the option of receiving a computer system worth $2300 or accepting a chance to win either a luxary vacation worth $5000 ora boat worth $8000.If the second option is chosen the contestant"s probability of winning the vacation or the boat are .20 and .15 respectively
A If the con testant were to turn down the computer system and go for one of the other prizes what would be the expected winnings/
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To calculate the expected winnings, you need to multiply the value of each potential outcome by its probability of occurring, and then sum these values.
Option 1: Computer system worth $2300 (Probability = 1)
Expected winnings for option 1 = ($2300 * 1) = $2300
Option 2: Luxury vacation worth $5000 (Probability = 0.2)
Expected winnings for option 2 = ($5000 * 0.2) = $1000
Option 3: Boat worth $8000 (Probability = 0.15)
Expected winnings for option 3 = ($8000 * 0.15) = $1200
Now, let's calculate the overall expected winnings:
Expected winnings = Expected winnings for option 1 + Expected winnings for option 2 + Expected winnings for option 3
= $2300 + $1000 + $1200
= $4500
Therefore, if the contestant were to turn down the computer system and go for either the luxury vacation or the boat, the expected winnings would be $4500.