In order to attract more customers, the Hyacintho Cactus Bar and Grill in downtown Ottawa organizes a game night, hosted by their star employee Tan Tran.

After paying $26, a player gets two questions P and Q. If the player gives the correct answer to question P, this player wins $30; if the player gives the correct answer to question Q, this player wins $60. A player can choose between the following two options:

1. Start with question P. In this case, the player is allowed to answer question Q only if the answer to question P is correct.

2. Start with question Q. In this case, the player is allowed to answer question P only if the answer to question Q is correct.

Elisa decides to play this game. The probability that Elisa correctly answers question P is equal to 1/2, whereas she correctly answers question Q with probability 1/3. The events of correctly answering are independent.

• Assume Elisa chooses the first option. Define the random variable X to be the amount of money that Elisa wins (this includes the $26 that she has to pay in order to play the game). Determine the expected value E(X). Show your work.

• Assume Elisa chooses the second option. Define the random variable Y to be the amount of money that Elisa wins (this includes the $26 that she has to pay in order to play the game). Determine the expected value E(Y ). Show your work.