A certain game involves tossing 3 fair coins, and it pays 8¢ for 3 heads, 3¢ for 2 heads, and 1¢ for 1 head. Is 3¢ a fair price to pay to play this game? That is, does the 3¢ cost to play make the game fair? What are the expected winnings for this game in cents?

Q: Consider this simple game. You pick a card randomly. If you get an Ace, you win $10. Otherwise, you…

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Q: A game involves tossing two coins and receiving 70¢ if they are both heads. What is a fair price to…

A: When we toss two coins the sample space is S={HH,HT,TH,TT} n(S)=4 Let E be the event of getting both…

Q: You are playing a game in which a single die is rolled. If a 2 or a 5 come up, you win $60;…

A: We will make a probability distribution of the winning values outcome 1 2 3 4 5 6…

Q: Explain Bayes theorem with examples and applications.

A: BAYES' THEOREM It is a concept used to determine the conditional probability of events. Consider two…

Q: At a local fair, a raffle is being held. There were 1,067 tickets were sold for $10 each. There is…

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Q: Consider rolling a 6-sided die. The outcome of interest is the number of dots that appears on the…

A: Rolling a 6-sided die, The possible outcomes are 1,2,3,4,5,6Since each of these is equally likely,…

Q: Rafael is at the grand opening celebration of a supermarket. He spins a wheel with 10 equal-sized…

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Q: In a game, a man is paid P300 if he draws a jack or a queen and P500 if he draws a king or an ace…

A: Given In a game, a man is paid P300 if he draws a jack or a queen and P500 if he draws a king or an…

Q: How much profit should you make on a $14 bet if the payoff odds are

A: Let x be the profit.  The profit is obtained by multiplying bet amount with payoffs odd.  That is,…

Q: A charity organization is holding a raffle. Each ticket costs $14. One winner will win $1500, two…

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Q: You are playing a card game. If you pull an Ace you win $86, if you pull the King of hearts you win…

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Q: Suppose you play a coin toss game in which you win $1 if a head appears and lose $1 if a tail…

A: Given: It is given that heads come up 37 times and tails come up 63 times in the first 100 coin…

Q: What is the average number of points you would expect to lose if you roll the die 60 times? b.…

A: Given : Number of times die is rolled =50 Lose a point if 1 is rolled

Q: Colleen bets $1 on a 2 digit number. She wins $75 if she draws her number from the set of. all 2…

A: Given that - Colleen bets $1 on a 2 digit number. She wins $75 if she draws her number from the set…

Q: Roll a pair of four-sided dice. If the sum is 2 or 8, win $10. If the sum is 3 or 7, win $5.…

A: roll a four sided dice , outcomes: {1,2,3,4}   roll pair of four sided dice total outcomes = 4*4 =…

Q: Marleny is creating a game of chance for her family. She has 5 different colored marbles in a bag:…

A: From the provided information is  E(X)=-2*P(X=-2)+p*P(X=p)E(X)=-2*45+p*150=-85+p50=-8+pp=8

Q: Marlon is going to roll a six-sided die, and if he rolls a 3, he gets $10. It costs him $2 to enter…

A: Random variables are of 2 types, discrete and continuous. A discrete random variable can only take…

Q: A game involves tossing two coins and receiving 74 cents they are both heads. What is a fair price…

A: From the provided information, A game involves tossing two coins. Total outcomes tossing two coins =…

Q: If the game is fair, the woman should play $ to play. (Type an integer or a decimal. Round to the…

A: Let X be the random variable that amounts to paid or loss. The game is of standard deck.There are 52…

Q: You play a game by drawing a card from a standard deck then replacing the drawn card. If you draw a…

A: If a queen or a king is drawn then the winning amount is Php 500 If a Ace is drawn then the winning…

Q: at a casino, you throw a fair 4 sided dice whose sides are labeled 1, 2, 3 and 4.   If you land on…

A: Solution: Total number of sides in a fair dice is = 4         Sides labeled as = 1, 2, 3, 4 The…

Q: Q13. In a bet, you have 40% probability of losing $15. What should the potential winnings from such…

A: From. The above data  We are given that the  n= 15 P = 0.40

Q: ou are on a TV show. You have been asked to either play a dice game five times or accept a $150…

A: Expectation of a Random Variable: The expectation of a random variable X, denoted by E(X), is…

Q: Assuming you were lucky enough to win and the pay off odds were 35:1, how much money would you get…

A: Given data: The given odd ratio is 35:1. The meaning of the given odd ratio is that for every $1 we…

Q: Let’s examine the following game with a fair die. You select a number (not necessarily an integer).…

A: Scenario:You select a number (not necessarily an integer). I roll a fair die, and pay you $10, minus…

Q: A die is rolled. If an odd number turns up, we win an amount equal to this number; if an even number…

A: The outcome of rolling a die is {1, 2, 3, 4, 5, 6}.

Q: The chance of winning Florida's Pick-6 Lotto game is 1 in approximately 23 million. Suppose you buy…

A: Random variables are of 2 types, discrete and continuous. A discrete random variable can only take…

Q: You pay $20 to enter a raffle.  The first ticket drawn wins $964, the second ticket drawn wins $522,…

A: The expectation of a discrete random variable X, denoted by E(X), is defined as a measure of central…

Q: A game is played by drawing one card at random from a standard 52-card deck. If the card is a…

A: We have given that the Total number of card in standard deck= 52 If the card is diamond, the player…

Q: In the casino a card game takes 1 dollar bets, players have a 46% chance of winning back their bets…

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Q: Consider the dice game in which 2 dice are rolled.  If the sum of the dice is 11, then your friend…

A: If the sum of the dice is 11, then your friend will give you $45; otherwise, you have to give your…

Q: 2. In a game, you have to roll a six-sided die and flip a coin. What is the probability of getting a…

A: In a game, six-sided die and coin was flipped. When flipping a coin, the outcomes are (Head, Tail).…

Q: In a gambling game, a woman is paid $7 if she draws a ten, a three, or a seven and $9 if she draws a…

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Q: You have a choice between two games. Game a said that you have a 0.864 probability of winning, and…

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Q: An American roulette wheel has 38 slots: 18 red, 18 black, and 2 green. What are the odds for the…

A: an american roulette wheel has 38 slots: 18 red , 18 black, 2 greennow , we know :-P(R)=P(landing in…

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.