Question: Expected Value: Suppose you attend a local summer fair event and a game proceeds as follows: You place an initial bet of $5 and receive one chance to hit the following target with a dart.

The probabilities of hitting each region of the target are depicted in the image. If you hit the central target (p=0.1), you receive your initial bet and win an additional $X. If you hit the second ring (p=0.2), you receive your initial bet and win an additional $Y. If you hit the outer ring (p=0.45), you receive your initial bet and win an additional $Z. If you miss the target entirely (p=0.25), you lose your initial bet of $5. For which of the following values of (X,Y, and Z), would you accept this bet? Explain your answer.

1. X=$10, Y=$5, Z=$0
2. X=$5, Y=$5, Z=$0
3. X=$4, Y=$2, Z=$0
4. X=$1.50, Y=$1.50, Z=$1
5. X=$15, Y=$0, Z=$0.

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