You are playing the new Lemon Game at Vegas. There are 3 windows in the slot machine. Window 1 displays only one of two choices: lemon or strawberry. Window 2 can display three choices: lemon, strawberry, or blueberry. Window 3 can display three choices: lemon, papaya, or cherry. Windows spin randomly and independent from each other. To win $1 you must have one lemon showing. To win $2, you must have two lemons, and to win the $5 jackpot, you must have all windows showing lemons.     Using a tree diagram, determine the sample space.   Determine the probability distribution. Let the random variable X represent the number of lemons displayed during one spin.   Calculate the mean and standard deviation of the distribution.   In four sentences or less, would you want to play this game if it cost $.50 per spin? Justify your answer using the expected value approach.

There are two biscuit tins on a shelf. the red tin contains three chocolate biscuits and seven plain biscuits. the bulue tin contains one chocolate biscuit and nine plain biscuits.  A childs reaches into the red tin and randomly selects a biscuit. The child returns that biscuit to the tin, shakes the tin, and then selects another biscuit. Find the porbability that both biscuits chosen are chocolate. one of the biscuits is plain and the other biscuit is chocolate. A second child chooses a biscuit from the blue tin. the child eats the biscuit and chooses another one from the blue tin

A particular two-player game starts with a pile of diamonds and a pile of rubies. Onyour turn, you can take any number of diamonds, or any number of rubies, or an equalnumber of each. You must take at least one gem on each of your turns. Whoever takesthe last gem wins the game. For example, in a game that starts with 5 diamonds and10 rubies, a game could look like: you take 2 diamonds, then your opponent takes 7rubies, then you take 3 diamonds and 3 rubies to win the game.You get to choose the starting number of diamonds and rubies, and whether you gofirst or second. Find all starting configurations (including who goes first) with 8 gemswhere you are guaranteed to win. If you have to let your opponent go first, what arethe starting configurations of gems where you are guaranteed to win? If you can’t findall such configurations, describe the ones you do find and any patterns you see.

Two mining companies, Red and Blue, bid for the right to drill a field. The possible bids are $ 15 Million, $ 25 Million, $ 35 Million, $ 45 Million and $ 50 Million. The winner is the company with the higher bid.The two companies decide that in the case of a tie (equal bids), Red is the winner and will get the field.Company Red has ordered a geological survey and, based on the report from the survey, concludes that getting the field for more than $ 45 Million is as bad as not getting it (assume loss), except in case of a tie (assume win). (1)Considering all possible combinations of bids, formulate the payoff matrix for the game. (2) Verify: does the game have a saddle point? (3)Construct a linear programming model for Company Blue in this game.

Raina is playing a game in which she spins a spinner with 6 equal-sized slices numbered 1 through 6. The spinner stops on a numbered slice at random. This game is this: Raina spins the spinner once. She wins $1 if the spinner stops on the number 1, $3 if the spinner stops on the number 2, $5 if the spinner stops on the number 3, and $7 if the spinner stops on the number 4. She loses $8 if the spinner stops on 5 or 6. (If necessary, consult a list of formulas.) (a) Find the expected value of playing the game. dollars (b) What can Raina expect in the long run, after playing the game many times? O Raina can expect to gain money. She can expect to win dollars per spin. O Raina can expect to lose money. She can expect to lose dollars per spin. O Raina can expect to break even (neither gain nor lose money). Submit O

Tardigrades, or water bears, are a type of micro-animal famous for their resilience. In examining the effects of radiation on organisms, an expert claimed that the amount of gamma radiation needed to sterilize a colony of tardigrades no longer has a mean of 1150 Gy (grays). (For comparison, humans cannot withstand more than 10 Gy.) A random sample of 25 tardigrade colonies found that the amount of gamma radiation needed to sterilize a colony had a sample mean of 1133 Gy, with a sample standard deviation of 02 Gy. Assume that the population of amounts of gamma radiation needed to sterilize a colony of tardigrades is appraximately normally distributed. Complete the parts below to perform a hypothesis test to see if there is enough evidence, at the 0.05 level af significance, to support that H, the mean amount of gamma radiation needed to sterilize a colony of tardigrades, is not equal to 1150 Cy. (a) State the null hypothesis H, and the alternative hypothesis H, that you would use for…

Each student's locker combination at Guion Creek Middle School contains three numbers ranging from 0 to 49 Alex and Dante are playing a game with their locker combinations.  Alex is giving Dante hints to his locker combination to see if Dante can guess the combination   A.  Alex's first hint is that the first number in the combination is a 3,4, or a 5.  How many possible choices are there for the 1st Number?   B.  The hint for the second number is that it is NOT a 3 or a 4.  How many possible numbers are there for the 2nd number?   C.  The hint for the third number is that it is an odd number.  How many possible numbers are there for the 3rd number? D. How many possible combinations are there? E.  What is the probability that 3:32:7 is Alex's combination?  leave your answer as a fraction with NO spaces Answer for A:____________ Answer for B:______________ Answer for C:____________ Answer for D:________________ Answer for E:_________________

You need to borrow money for gas, so you ask your mother and your sister. You can only borrow money from one of them. Before giving you money, they each say they will make you play a game. Your sister says she wants you to spin a spinner with two outcomes, blue and red, on it. She will give you $⁢10 if the spinner lands on blue and $⁢20 if the spinner lands on red. Your mother wants you to spin a spinner with six outcomes, numbered 1 through 6, on it. She will give you $3 ⁢three times the number that the spinner lands on. Determine the expected value of each game and decide which offer you should take. The expected value for your sister's game: $$ Anticipated value for your mother's game: $$ Which offer should you take? Your sister's offer or your mother's offer?

This is a game for two people. Taking alternate turns, choose a whole number from 1 to 8. Keep a running total. (For example, if you pick 2 and your opponent picks 6, the total is now 8. Then maybe you pick 5, so now that total is 13, and so on.) The object of the game is to make the score exactly 64 on your turn. (If it is your turn and the running total at that point is 62, you would say 2, making the score 64, and you would be the winner.) You are going to choose the first number. What number should you pick to guarantee a win for yourself, and what strategy should you follow?

Ms. Bell's mathematics class consists of 11 sophomores, 6 juniors, and 15 seniors. How many different ways can Ms. Bell create a 3-member committee of juniors if each junior has an equal chance of being selected?