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Answer:
Part a) Alyssa's expectation is equal to $0.33
Part b) Gabriel's expectation is equal to -$0.33
Step-by-step explanation:
we know that
The expected value is the probability of winning multiplied by the value you get when you win, plus the probability of losing multiplied by the value you get when you lose (which is negative as it is a loss).
Part a) Determine Alyssa's expectation
we know that
1) If Alyssa rolls a 1, 2, or 3, Gabriel gives Alyssa $4
The probability is 3/6
so
we have
2) If Alyssa rolls a 4, or 5, Gabriel gives Alyssa $1
The probability is 2/6
so
we have
3) if Alyssa rolls a 6, she gives Gabriel $12
The probability is 1/6
so
we have
---> is negative because is a loss
therefore
Alyssa's expectation is equal to
Part b) Determine Gabriel's expectation
we know that
1) If Alyssa rolls a 1, 2, or 3, Gabriel gives Alyssa $4
<u>Is a loss for Gabriel</u>
The probability is 3/6
so
we have
---> is negative because is a loss
2) If Alyssa rolls a 4, or 5, Gabriel gives Alyssa $1
<u>Is a loss for Gabriel</u>
The probability is 2/6
so
we have
---> is negative because is a loss
3) if Alyssa rolls a 6, she gives Gabriel $12
<u>Is a win for Gabriel</u>
The probability is 1/6
so
we have
therefore
Gabriel's expectation is equal to
