2.We play a game with a deck of 52 regular playing cards, of which 26 are red and 26are black. They're randomly shuffled and placed face down on a table. You have the optionof "taking" or “skipping" the top card. If you skip the top card, then that card is revealedand we continue playing with the remaining deck. If you take the top card, then the gameends; you win if the card you took was revealed to be black, and you lose if it was red. If weget to a point where there is only one card left in the deck, you must take it. Prove that youhave no better strategy than to take the top card – which means your probability of winningis 1/2.Hint: Prove by induction the more general claim that for a randomly shuffled deck of n cardsthat are red or black - not necessarily with the same number of red cards and black cards -there is no better strategy than taking the top card.

Given a game with a deck of 52 regular playing cards, of which 26 are red and 26 are black.

Answered: 2. We play a game with a deck of 52…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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This is one question, but I couldn't fit it all in one photo so I attached two photos.
At a county fair, you pay $2 to play the following game: You are given a fair coin, and two bags standin front of you, labelled Bag A and Bag B. You flip a coin: If your coin lands Heads, you pick a ballfrom Bag A. If your coin lands tails, you pick a ball from Bag B. Each ball has a dollar value written onit, and you win the number of dollars shown on the ball. • Bag A contains four (4) balls in total: Three (3) balls show $1, and one (1) ball shows $5.• Bag B contains three (3) balls in total: Two (2) balls show $2, and one (1) ball shows $3.You WIN money if you leave with more money than you started with. You LOSE money if you leavewith less money than you started with. You BREAK EVEN if you leave with the same money that youstarted with.Let H denote the event that you flip heads, T denote the event that you flip tails, W the event that youwin, and L the event that you lose.(i) You pay to play exactly one game. What is the probability that you WIN given thatyou flipped a Heads?(ii)…
Laura has a bag with 8 balls numbered 1 through 8. She is playing a game of chance. This game is this: Laura chooses one ball from the bag at random. She wins $1 if the number 1 is selected, $2 if the number 2 is selected, $5 if the number 3 is selected, $6 if the number 4 is selected, $8 if the number 5 is selected, and $10 if the number 6 is selected. She loses $14 if 7 or 8 is selected. (a) Find the expected value of playing the game. dollars (b) What can Laura expect in the long run, after playing the game many times? (She replaces the ball in the bag each time.) O Laura can expect to gain money. She can expect to win dollars per selection. O Laura can expect to lose money. She can expect to lose dollars per selection. O Laura can expect to break even (neither gain nor lose money). X
James placed a $25 bet on a red and a $5 bet on the number 33 (which is black) on a standard 00 roulette wheel. -if the ball lands in a red space, he wins $25 on his 'red' but loses $5 on his '33' bet - so he wins $20 -if the ball lands the number 33, he loses $25 on his 'red' bet but wins $175 on his '33' bet: He wins $150 -if the ball lands on a spae that isn't red and isnt 33 he loses both bets, so he loses $30 So for each spin; he either wins $150, wins $20, or loses $30 -probability that he wins $150 is 1/38 or .0263 -probability that he wins $20 is 18/38 or .4737 -probability that he loses $30 is 19/38 or .5000 let X = the profit that james makes on the next spin x P (X=x) x*P(X=x) x^2*P(X=x) 150 .0263 3.945 591.75 20 .4737 9.474 189.48 -30 .5000 -15.000 450.00 sum (sigma) 1.000 -1.581 1231.23 u (expected value)= -$1.581 variance = 1228.73044 standard deviation = 35.053 FILL IN THE BLANK if you play 2500 times, and Let, x (x bar)= the mean winnings (or…
5. Divide and conquer. You're again facing your friend, Brenda, in a "candy-off” game involving a pile of 100 caramels and the winner's prize: one peppermint patty. (Like before, you still LOVE peppermint patties!). On their turn, each player can remove a
You have been asked to play a card game. A card is dealt from a complete deck offifty-two cards (no jokers). A deck has 4 aces, 4 kings, 4 queens, 4 jacks, and 36 other cards.It works like this:• If the card is a ace, you lose $4.• If the card is a king or jack, you lose $10.• If the card is a queen, you win $8.• If the card is anything else, you win $1.Find the expected value of the game. Write the excepted value rounded to the nearest cent
General: Deck of Cards: You draw two cards from a standard deck of 52 cards without replacing the first one before drawing the second. Are the outcomes on the two cards independent? Why? Find P (3 on 1st card and 3 on 2nd). Find P (10 on 1st card and 3 on 2nd).
A standard deck of cards has 52 cards in four suits: spades, hearts, diamonds, and clubs. Spades and clubs are black; hearts and diamonds are red. Each suit has 13 cards: 2 through 10, Jack, Queen, King, Ace. The "face cards" are the Jack, Queen, and King. Robby Billity shuffles a standard deck and draws one card. Then Robby Replaces the card, shuffles again, and draws another card. He repeats this procedure for a total of 1000 draws. About how many times would we expect Robby to draw these cards? A) the ace of spades B) a face card in any suit
20 a-d
In the board game Clue, the object of the game is to determine the which character is the murderer, whichweapon was used and in which room the murder took place (e.g., “Colonel Mustard with the Candlestickin the Library”). There are 6 different characters, 6 weapons, and 9 rooms. How many different outcomesare possible?

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