The game of craps is played with two dice. The player rolls both dice and wins immediately if the outcome (the sum of the faces) is 7 or 11. If the outcome is 2, 3, or 12, the player loses immediately. If he rolls any other outcome, he continues to throw the dice until he either wins by repeating the first outcome or loses by rolling a 7.

For his Carnival project, Chester designed a game where players pick a random marble from a bag. In the bag there are 2 pink marbles, 10 green marbles, and 8 white marbles. If players draw a pink marble they get a large candy bar prize, if they draw a green marble they get a small lollipop prize, and if they draw a white marble they get a fist bump. Chester purchased a set of 16 candy bars for $12 and a bag of 200 lollipops for $20. Answer the following questions: What is Chester's expected cost per game? $  If Chester plans for 40 people to play his game, How many candy bars should he expect to give out?  How many lollipops should he expect to give out?

A restaurant will select 1 card from a bowl to win a free lunch. Jimmy puts 10 cards in the bowl. The bowl has a total of 150 cards in it when they do the drawing. What are the odds of Jimmy winning a free lunch?

Four men and a monkey spend the day gathering coconuts on a tropical island. After they have all gone to sleep at night, one of the men awakens and, not trusting the others, decides to take his share. He divides the coconuts into four equal piles, except for one remaining coconut, which he gives to the monkey. He then hides his share, puts the other piles together, and goes back to sleep. Each of the other men awakens during the night and does likewise, and every time there is one coconut left over for the monkey. In the morning all the men awake, divide what's left of the coconuts into four, and again there is one left over that is given to the monkey. Find the minimum number of coconuts that could have been in the original pile.

Station 4: Dice Wars - Instructions "EFFERVESCENT" roll two six-sided dice and add the outcomes to calculate their score; "SCINTILLANT" roll two six-sided dice and multiply the outcomes to calculate their score. A. Calculate the probability of "EFFERVESCENT" getting a sum of 6. B. Calculate the probability of "SCINTILLANT" getting a product of 6.

Annie and Bert play the following game. They shuffle a deck of 52 cards. Annie flips the cards one by one until she finds a red ace. After that Bert takes the remaining deck and flips the cards one by one until he finds the other red ace. Annie wins if she flipped fewer cards than bert, bert wins if he flipped fewer cards than Annie. It's a tie if they draw the same number of cards.  X1 = number of cards Annie flipped, X2= number of cards Bert flipped.      X3= 53- X1 - X2. How can you show that (X1, X2, X3) is exchangeable? Who has a higher probability of winning this game?

You have four pairs of socks, one pair each of red, blue, white, and green. Each morning, you reach into the drawer and pick out two random socks. How many days could go by before you picked exactly the same two colors of socks again?

Billy and Joe are buddies that think they can outsmart the casino by splitting each other’s profits. They decided to play a game by the name of Baccarat. They both have $1200 and their goal is to leave once they double their money. In Baccarat, the Banker's or Player’s hand will win 45% of the time. Ties win 10% of the time. The goal in baccarat is to have the hand you’re betting on, either the player or the banker, be the best hand of the two dealt. The winning hand is the one with a score where the final digit is the closest to nine. Face cards are worth zero, and aces count as one. There are 8 decks in a shoe. Billy and Joe came up with a betting strategy/sequence and assigned “teams”. Billy will ALWAYS bet on “Player” whereas Joe will always bet on “Banker”. The sequence goes as follows: Billy: 12113 Joe: 21221Billy: $100, $200, $100, $100, $300 = $900Joe: $200, $100, $200, $200, $100 = $900The remaining $300 that Billy and Joe have will go towards taking turns on betting $5 on the…

Suppose that you and a friend are playing cards and decide to make a bet. If you draw two clubs in succession from a standard deck of 52 cards without replacing the first card, you win $⁢40. Otherwise, you pay your friend $⁢10. If the same bet was made 25 times, how much would you expect to win or lose? Round your answer to the nearest cent, if necessary. Win: Lose:

In this game, two chips are placed in a cup. One chip has two red sides and one chip has a red and a blue side. The player shakes the cup and dumps out the chips. The player wins if both chips land red side up and loses if one chip lands red side up and one chip lands blue side up. The cost to play is $4 and the prize is worth $6. Is this a fair game.