1- For example, suppose that you ask your father for some extra money. Instead of just giving you the money, he offers to flip a coin. If the coin lands "heads" – you win – and he will give you $20. If it lands “tails", you lose, and you receive nothing. In this example, we would say that the payout associated with the event that the coin lands "heads" is $20, and the payout associated with "tails" is $0. Before accepting your dad's offer, you turn to your mother and ask her for some extra money. Having overheard the conversation with your father, she makes a different offer. She will role a die, and give you $3 for every spot that turns up. (That is, if she rolls a 1, she will give you $3; if she rolls a 2, she will give you $6.00 (= 2 x $3.00), ... if she rolls a 6, she will give you $18 (= 6 x $3.00)). At this point you realize two things: First, you realize your parents are both very weird. Second, (since your mother and father won't both give you money) you realize that you need some way to compare the two offers. So which of these offers should you take? Which is the better offer? 2-A card is drawn at random from a deck consisting of cards numbered 2 through 10. A player wins 1 dollar if the number on the card is odd and loses 1 dollar if the number if even. What is the expected value of his winnings?

Whenever Suzan sees a bag of marbles, she grabs a handful at random. She has seen a bag containing three red marbles, five green ones, three white ones, and one purple one. She grabs five of them. Find the probability of the following event, expressing it as a fraction in lowest terms. She has no more than one white one.

The Gambler's Fallacy is the idea that past events can affect future behavior. The fallacy often generates real financial consequences for those who like to take their chances at gambling, which, in turn, reaps financial benefits for gambling businesses like casinos or race tracks. Being a person who enjoys playing dice games, you want to test the Gambler's Fallacy using a six-sided die. You toss the die 300 times with the following results. Roll 1 2 3 4 5 6 Frequency 54 49 50 51 51 45 Find the value of the chi-square test statistic for this scenario.

A "psychic" runs the following ad in a magazine: Expecting a baby? Renowned psychic will tell you the sex of the unborn child from any photograph of the mother.Cost, $20. Money‑back guarantee. This may be a profitable con game. Suppose that the psychic simply replies "boy" to all inquiries. In the worst case, everyone who has a girl will ask for her money back.  Sex of child Probability The psychic's profit Boy 0.51   Girl 0.49   The expected value of the psychic's profit is the average dollar amount kept from customer (ignoring any postage costs).   Find the expected value of the psychic's profit by filling in the boxes below with you answers. Use decimal notation. If your answer is not a whole number, round to the nearest tenths place.  Psychic's profit for Boy: $  Psychic's profit for Girl: $ Expected value: $

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Suppose you decided to play a gambling game. In order to play the game there is a $1.00 dollar fee to play. If you roll a 1, 2, or 3 you win nothing (i.e., your net profit is $-1.00). If you roll a 4 or 5, you win $2.50 (i.e., your net profit is $1.50). If you roll a 6 you win $4.00 (i.e., your net profit is $3.00).Use the information described above to construct a probability distribution table for the random variable xx which represents the net profit of your winnings. Note: Be sure to enter your probabilities as reduced fractions. Die Roll xx P(x)P(x) Roll a 1, 2, or 3      Roll a 4 or 5      Roll a 6      Find the amount you would expect to win or lose each time you played the game. Round your final answer to two decimal places.μ=

Previous q Determine the number of outcomes in the event. Decide whether the event is a simple event or not. You randomly select one card from a standard deck of 52 playing cards. Event B is selecting a four of diamonds. Event B has outcome(s). Is the event a simple event? because event B has one outcome.

Ashley is holding a fair six-sided die and a fair coin. If Ashley rolls the die once and then flips the coin, what is the probability that the die will show a 5 and the coin will come up tails?

Suppose you are invited to play a game in which you bet $1 on any number from 000 to 299. If your number comes up, you get $75. Find the expected winnings. Expected winnings = $ (Type an integer or decimal rounded to the nearest cent as needed.)

The Dice game of “Pig” can be played with the following rules. Roll two six-sided dice. Add the face values together. Choose whether to roll the dice again or pass the dice to your opponent. If you pass, then you get to bank any points earned on your turn. Those points become permanent. If you roll again, then add your result to your previous score, but you run the risk of losing all points earned since your opponent had rolled.  Continue to roll as much as you want. However, once a “1” comes up on either die, your score is reduced to 0, leaving you only with points that you have previously "banked." Furthermore, you must pass the dice to your opponent. The first person to 100 points is the winner. When a player rolls two dice, the possible outcomes are as follows:   Die #2 Roll Roll a 1 Roll a 2 Roll a 3 Roll a 4 Roll a 5 Roll a 6 Die #1 Roll Roll a 1 0 0 0 0 0 0 Roll a 2 0 4 5 6 7 8 Roll a 3 0 5 6 7 8 9 Roll a 4 0 6 7 8 9 10 Roll a 5 0 7 8 9 10 11 Roll a 6 0 8 9 10…