Jose has a deck of 10 cards numbered 1 through 10. He is playing a game of chance.This game is this: Jose chooses one card from the deck at random. He wins an amount of money equal to the value of the card if an even numbered card is drawn. He loses $6 if an odd numbered card is drawn.(a) Find the expected value of playing the game.dollars(b) What can Jose expect in the long run, after playing the game many times?(He replaces the card in the deck each time.)Jose can expect to gain money.Hecanexpecttowindollarsperdraw.Jose can expect to lose money.Hecanexpecttolosedollarsperdraw.Jose can expect to break even (neither gain nor lose money).

A game in a casino consists of drawing one card from a standard deck of cards. If the player  Draws an ace, they win €20Draws a face card(Jack, Queen,King) they win €10Draws a 10, they win €5Draws a 2, they lose €5Draws anything else(3 - 9), they win nothingCalculate the expected value of the game (Give your answer correct to 2 decimal places)

Justin is playing a game of chance in which he rolls a number cube with sides numbered from 1 to 6. The number cube is fair, so a side is rolled at random.This game is this: Justin rolls the number cube once. He wins $1 if a 1 is rolled, $2 if a 2 is rolled, $3 if a 3 is rolled, and $4 if a 4 is rolled. He loses $6.50 if a 5 or 6 is rolled.(If necessary, consult a list of formulas.)(a) Find the expected value of playing the game.dollars(b) What can Justin expect in the long run, after playing the game many times?Justin can expect to gain money.Hecanexpecttowindollarsperroll.Justin can expect to lose money.Hecanexpecttolosedollarsperroll.Justin can expect to break even (neither gain nor lose money).

Ravi has a bag with 8 balls numbered 1 through 8. He is playing a game of chance.This game is this: Ravi chooses one ball from the bag at random. He wins $1 if the number 1 is selected, $2 if the number 2 is selected, $5 if the number 3 is selected, $6 if the number 4 is selected, $8 if the number 5 is selected, and $10 if the number 6 is selected. He loses $14 if 7 or 8 is selected.(If necessary, consult a list of formulas.)(a) Find the expected value of playing the game.dollars(b) What can Ravi expect in the long run, after playing the game many times?(He replaces the ball in the bag each time.)Ravi can expect to gain money.Hecanexpecttowindollarsperselection.Ravi can expect to lose money.Hecanexpecttolosedollarsperselection.Ravi can expect to break even (neither gain nor lose money).

Shen is playing a game of chance in which he rolls a number cube with sides numbered from 1 to 6. The number cube is fair, so a side is rolled at random.This game is this: Shen rolls the number cube once. He wins $1 if a 1 is rolled, $2 if a 2 is rolled, and $3 if a 3 is rolled. He loses $2.50 if a 4, 5, or 6 is rolled.(a) Find the expected value of playing the game.dollars(b) What can Shen expect in the long run, after playing the game many times?Shen can expect to gain money.Hecanexpecttowindollarsperroll.Shen can expect to lose money.Hecanexpecttolosedollarsperroll.Shen can expect to break even (neither gain nor lose money).

Now, can you calculate the expected value of X (where X is the money won by the player after playing the game once)?X (Money won after playing once) Probability+150 0.133−10 0.867You can use this probability distribution to find the answer