Becca plays a game in which she can purchase a ticket. Each ticket has several chances, or "catches," to win money.The table below shows the probability of winning at each stage, and how much money the ticket can win at each catch. Every time Becca plays the game, her ticket is played through each catch, which means she can win money at each stage.Catch Probability WinningsCatch 0 40% $1Catch 1 45% $5Catch 2 12% $10Catch 3 3% $25Given the probabilities and payout values in this table, what is the expected value of Becca's ticket?a.)$4.60b.)$1.20c.)$10.25d.)$41.00

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

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

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

At a raffle, 1500 tickets are sold at $2.00 each for four prizes of $500, $250, $150, and $75. You buy one ticket. What is the expected value of your gain?X $498 $248 $148 $73 -$2P(X) 1/1500 1/1500 1/1500 1/1500 1496/1500Group of answer choices$193$1.35-$193-$1.35

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).