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).

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).

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).

John has a deck of 10 cards numbered 1 through 10. He is playing a game of chance.This game is this: John chooses one card from the deck at random. He wins an amount of money equal to the value of the card if an odd numbered card is drawn. He loses $3.40 if an even numbered card is drawn.(If necessary, consult a list of formulas.)(a) Find the expected value of playing the game.dollars(b) What can John expect in the long run, after playing the game many times?(He replaces the card in the deck each time.)John can expect to gain money.Hecanexpecttowindollarsperdraw.John can expect to lose money.Hecanexpecttolosedollarsperdraw.John can expect to break even (neither gain nor lose money).

In American roulette, the wheel has 38 number: 00, 0, 1, 2, 3, ..., 35, 36 marked on equally spaced slots. If a player bets $10 on a single number and wins, then the player gains $350 otherwise the player loses the $10.This means, that X is either $350 or -$10.What is the expected value of this game?Group of answer choices$0.53$18.95-$18.95-$0.53

Suppose we change the game’s rules to the following:Outcome Prize4 red balls +1504 blue balls -150Any other outcome -10What will be the expected value for X (the amount of money won by a player after playing the game once)?-2.5-5+2.5+7.5