From the list below, supply the words needed to complete the paragraph. Some words will not be used. Dastardly, gist, entity, jaded, ogre, bandy, charisma. The ______ athlete, accustomed to winning first place, wanted to be happy with her third-place trophy, but deep down, she felt that months of intensive training had gone to waste. On the bus ride home, she refused to _____ compliments or even joke about the race with her teammates. She could think only about the _______ runner who intentionally tripped her early in the race and likely cost her the win. Myra could not believe that such an unsportsmanlike _______ was allowed to compete in track meets.

From the list below, supply the words needed to complete the paragraph. Some words will not be used.

$$\begin{matrix} \text{influx} & \text{pinnacle} & \text{sedentary} & \text{junta}\\ \text{conducive} & \text{rigorous} & \text{stricture}\\ \end{matrix}$$

Heather knew that she would need to impose some ______ on her eating habits in order to comply with her _______ training regimen in the weeks before the	marathon. Timing was crucial; in order to place well, Heather would need to reach the _____ of her fitness on the day of the race. Several days of rest before the race will be ______ to her winning, but until that time, no one would be able to regard Heather as ______; if she's not sleeping, she will be running.

The gaming commission is introducing a new lottery game called Infinite Progresso. The winner of the Infinite Progresso jackpot will receive $1,000 at the end of January,$2,000 at the end of February, $3,000 at the end of March, and so on up to$12,000 at the end of December. At the beginning of the next year, the sequence repeats starting at $1,000 in January and ending at$12,000 in December. This annual sequence of payments repeats indefinitely. If the gaming commission expects to sell a minimum of 1 million tickets, what is the minimum price they can charge for the tickets to break even, assuming the commission earns 6 percent/year/month on its investments and there is exactly one winning ticket.

In New Jersey’s Pick 4 lottery game, you pay 50 cents to select a sequence of four digits, such as 7273. If you win by selecting the same sequence of four digits that are drawn, you collect $2788. a. How many different selections are possible? b. What is the probability of winning? c. If you win, what is your net profit? d. Find the expected value. e. An example showed that if you bet 50 cents in the New Jersey Pick 3 game, your expected value is -22.5 cents. Which is the better game: New Jersey’s Pick 3 game or Pick 4 game? Why?

Howie Long has just learned he has won a $500,000 prize in the lottery. The lottery has given him two options for receiving the payments. (1) If Howie takes all the money today, the state and federal governments will deduct taxes at a rate of 46% immediately. (2) Alternatively, the lottery offers Howie a payout of 20 equal payments of$36,000 with the first payment occurring when Howie turns in the winning ticket. Howie will be taxed on each of these payments at a rate of 25%

Instructions

Assuming Howie can earn an 8% rate of return (compounded annually) on any money invested during this period, which payout option should he choose?

Making your vote count. Democratic and Republican presidential state primary elections are highlighted by the difference in the way winning candidates are awarded delegates. In Republican states, the winner is awarded all the state's delegates; conversely, the Democratic state winner is awarded delegates in proportion to the percentage of votes. This led to a Chance (Fall 2007) article on making your vote count. Consider the following scenario where you are one of five voters (for example, on a county commission where you are one of the five commissioners voting on an issue). Assume each commissioner is equally likely to vote for or against. Assign reasonable probabilities to the sample points, part a.

In the Pennsylvania Lottery's Daily Number (Evening) game, a three-digit number between 000 and 999 is chosen each day. The favorite number among players is 000, which on May 16, 2011, was the winning number for the 15th time since 1980. (a) Find the number of times that 000 would be expected to win in 32 years of play. (Assume that the game is played 365 days a year.) (b) In 2003, a Daily Number (Midday) drawing was added. The number 000 has occurred four times. Find the number of times that 000 would be expected to win in 10 years of play. (Assume that the game is played 365 days a year.)

Every contestant on a game show has a 40% chance of winning. In the simulation below, the numbers 1-4 represent a winner, and the numbers 5-10 represent a nonwinner. Numbers were generated until one that represented a winner was produced. Trial 1: 7, 4 Trial 2: 6, 5, 2 Trial 3: 1 Trial 4: 9, 1 Trial 5: 3 Trial 6: 8, 8, 6, 2 Trial 7: 2 Trial 8: 5, 9, 4 Trial 9: 10, 3 Trial 10: 1 Based on the simulation, what is the experimental probability that it will take exactly 4 contestants to get a winner?

From the list below, supply the words needed to complete the paragraph. Some words will not be used. charisma, efface, ogre, advocate, gist, bandy, mesmerize. Joan, who _____ the cleanup of the James River, is always trying to gain supporters for her cause. The usual _____ of her speech focuses on the effects of the river's pollution on future generations. Her eloquent speech _____ audiences, and her _____ helps her to win the hearts of people who are not even affected by the James River. Joan hopes someday to _____ the irresponsible dumping practices that continue to foul the James River.

A gambler makes a series of bets with probability p of winning and probability q > p of losing each bet. He decides to play until he has either won $M_{1}$ dollars or lost $M_{2}$ dollars, where $M_{1}$ and $M_{2}$ are positive integers. He has a choice of betting 1 dollar at a time or of betting 1/2 dollar at a time. Show that he is more likely to win $M_{1}$ dollars before losing $M_{2}$ dollars if he bets 1 dollar at a time than if he bets 1/2 dollar at a time. What generalization of this result seems plausible?

The following problem is sometimes called “The Monty Hall Game Show Problem.” You are a contestant on a game show and have won a shot at the grand prize. Before you are three closed doors. Behind one door is a brand new car. Behind the other two doors are consolation prizes. The location of the prizes is randomly selected. The game show host asks you to select a door, and you pick one. However, before revealing the contents behind your door, the game show host reveals one of the other doors with a consolation prize. At this point, the game show host asks if you would like to stick with your original choice or switch your choice to the other closed door. What choice should you make to optimize your chances of winning the car? Does it matter whether you stick with your original choice or switch doors?

Write a simulation program to solve the game show problem. Your program should make 10,000 simulated runs through the problem, randomly selecting locations for the prize, and then counting the number of times the car was won when sticking with the original choice, and counting the number of times the car was won when switching doors. Output the estimated probability of winning for both strategies. Be sure that your program exactly simulates the process of selecting the door, revealing one, and then switching. Do not make assumptions about the actual solution (for example, simply assuming that there is a 1/3 or 1/2 chance of getting the prize).

The exercise concerns the Monty Hall problem, in which a contestant chooses one of three doors; behind one of the doors is a car, and behind the other two are goats. After the contestant chooses a door, the host opens one of the other two doors that hides a goat. (Because there are two goats, the host can open a door that hides a goat no matter which door the contestant first chooses.) The host then gives the contestant the option of abandoning the chosen door in favor of the still-closed, unchosen door. For each strategy, what is the probability of winning the car? Make a random decision about whether to stay with the door initially chosen or switch to the unchosen, unopened door.

From the list below, supply the words needed In complete the paragraph. Some words will not be used. Beget, imbibe, chafe, feign, desist, glean, effrontery, educe. The psychologist used a form of hypnotism to ______ her patient's childhood memories. Little by little, the doctor _____ clues that might ______ the solution to Kate's disorder. Originally the doctor worried that Kate would ______ compliance and simply pretend to remember things, but the doctor could tell that the memories were real by the way in which they seemed to ______ the patient emotionally. One hour was all Kate could stand before her therapy had to _____ for the day.

A gambler believes that a strategy called “doubling up” is an effective way to gamble. The method requires the gambler to double the stake after each loss. Thus, if the initial bet is $1, after losing he will double the bet until he wins. After a win, he resorts back to a$1 bet. The result is that he will net $1 for every win. The problem, however, is that he will eventually run out of money or bump up against the table limit. Suppose that for a certain game the probability of winning is .5and that losing six in a row will result in bankrupting the gambler. Find the probability of losing six times in a row.