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).

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).

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

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).

Don Snow's life is in danger. Sirsea has sentenced him to death. But Don has demanded trial by programming, and he has named you as his champion to solve the following problem :A bag contains N balls indexed from 1 to N, ith of which has radius Ri.One instance of a game is played as follows :A number K is chosen.One ball is picked out from the bag, if this ball has index K, then the game stops, otherwise the game continues.The probability of a ball being picked from the bag is proportional to its radius.Your task is, to find the expected number of balls to be taken out of the bag for every K from 1 to N

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