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Alyssa and Gabriel play the following game. Alyssa rolls a die. If she rolls a​ 1, 2, or​ 3, Gabriel gives Alyssa ​$4. If Alyssa rolls a 4 or​ 5, Gabriel gives Alyssa ​$. ​However, if Alyssa rolls a​ 6, she gives Gabriel ​$23.
​a) Determine​ Alyssa's expectation.
​b) Determine​ Gabriel's expectation.