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Casino Lab – AP Statistics Casinos rely on the laws of probability and expected values of random Answer the following classical probability questions. 1.


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Explain your answer. 2-/25 - 80 - Welcome to the AP Statistics Casino Lab! Casinos rely on the laws of probability to guarantee them profits on a daily basis.


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The probabilities on the branches of the tree diagram should be the answer to parts (c)1, 2, and 3, respectively. Bonus: P. (win| (win at craps). 2.


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Casino Lab Solutions. STATION 1. CRAPS c. Probability Questions. The probabilities on the branches of the tree diagram should be the answer to parts (c​)1.


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How to Predict if You’re Going to Win (AKA: Probability)

Pick a door. What is the probability that you would obtain a sum of 2,3,or 12 on the first roll? AP Statistics Casino Lab 8. What is the probability that you would obtain a sum of 7 or a sum of 11 on the first roll? Record your results. At the end of each show, the contestant who had won the most money was invited to choose from among three doors: Door 1, Door 2, or Door 3. Have a partner act as the host and arrange the three cards behind the three doors at the table. AP Statistics Casino Lab 7. You must then decide to Stick or Switch. The main pockets, numbered from 1 to 36, alternate between red and black, but the pockets are not in numerical order around the wheel, and there are instances of consecutive numbers being the same color. At least one of the woman s children is a boy, and the man s older child is a boy. In many casinos, the dealer must hit until he or she has at least If the dealer s face-up card is a 10 or Face Card, what is P dealer points 17? In what proportion of games did you lose on your first roll? That is, What is P win 8? If you roll a 7, tally a LOSE and start a new game. If you roll any other number, continue rolling. Bonus 2: There are 3 prisoners, A, B, and C. That is, what is P 19 red in 38 spins? Blackjacks Twenty-ones 2. Intuition tells you it shouldn t matter whether you stick or switch Or is it? Calculate the Standard Deviation of the amount gained per play. But behind the other two were rather undesirable prizes -- say goats. This hand was called a "blackjack" and the name stuck to the game. To play the game, a croupier turns a round roulette wheel which has 38 separately numbered pockets in which a ball must land. What are the expected gain and standard deviation of the total amount gained for the two games? Consider the following tree diagram. You must collect data from each station in order to answer the questions. Theoretically, what proportion of games would result in a win on the first roll? Behind one of the three doors was a very nice prize. There is also a green pocket numbered 0 and a second green pocket marked Guess red or black and have your partner spin the wheel. Much of blackjack's popularity is due to the mix of chance with elements of skill, and the publicity that surrounds card counting keeping track of which cards have been played since the last shuffle. What is the probability you ll break even by betting on red-only in 38 spins? Find the probability you subsequently win the game, given your point is 8. The question is, is it better to stick with your original guess, or should you switch to the remaining door? Complete the probability distribution for X. Random variables are the raw material for statistical inference. Does there appear to be a better strategy? Show work. The dealer also receives 2 cards, one face-down and one face-up. As the game is currently played, a "blackjack" may not necessarily contain a jack at all. What is P Blackjack? What is the probability you would have picked the nice prize on the first selection? Suppose you play two games. A asks the warden to tell him the name of one of the others in his cohort who will be released. Casino stations are set up around the room. Bonus 1: A woman and a man who are unrelated each have two children.

You will get a chance to simulate playing several casinotype and other popular games of chance. Then, change strategies and use it on 10 trials.

In what proportion of games did you actually win? Your partner should open one of the doors you didn t pick, revealing a Jack. The goal is to have a point total as close to 21 as possible, or at least greater than the dealer s total.

Do you agree or disagree? X Find the Expected Gain per play. Suppose you roll a sum of 8 on your first roll. Feel free to move from station to station throughout the hour.

Which is more likely: that the man has 2 boys or source probability casino lab answers woman has 2 boys?

Simulate the game 20 times. Given that the face-up card is an ace Suppose the face-up card is a black jack spades or clubs. Casinos rely on the laws of probability and expected values of random variables to guarantee profits. While some probability casino lab answers walk away probability casino lab answers wealthy, most leave a little or a lot less wealthy than when they entered.

When blackjack was first introduced in the United States it was probability casino lab answers very popular, so gambling houses tried offering various bonus payouts to get the players to the tables.

Bonus: One strategy is to always bet red. Cards are worth face value except face cards which are worth probability casino lab answers points and the Ace, which is worth 1 or Let s consider some probabilities for the dealer s hand. What is P Twenty-one with two-cards? Theoretically, what proportion of games would result in a loss on the first roll?

However, having a total greater than 21 results in a learn more here and the player loses the hand.

What is the probability that you would roll again after your first roll? AP Statistics Casino Lab 5. However, be sure to play each game at least once. AP Statistics Casino Lab 3. Note whether or not you win.

Two of them will be released and one will be executed. Pick a strategy and use it on 10 trials.

What is P red? Suppose one card is dealt face-down and one card is face-up. Assume we are dealing without replacement from a single, well-shuffled deck. Regardless of what you originally choose, what is P Car if you Switch?

If the sum is 7 or 11, tally a WIN and probability casino lab answers a new probability casino lab answers. Count the number of heads.

Players may choose to hit or get another card to raise their point total. As the question in not directly about A's fate, the warden obliges and says, truthfully, "B will be released. The contestant selected a door. Is it better to Switch or to Stay? He then gave the contestant the option of sticking with the door she had originally selected or switching to the other, unrevealed, door. Deal a hand, check the result, and record whether or not it was a true blackjack, or twenty-one. If you roll your Point value, tally a WIN and start a new game. AP Statistics Casino Lab 6. While an individual outcome is unpredictable for a given random variable, probability theory tells us that there is a certain type of regularity or predictability in the results. Source: Wikipedia Basic Rules: To play the game, each player is dealt 2 cards face-up. There are 3 cards at this station, the Ace represents a nice prize, while the two Jacks represent goats. One such bonus was a to-1 payout if the player's hand consisted of an ace and a black Jack either the Jack of clubs or the Jack of spades. We have been studying random variables for some time, but we made them the center of our attention in Chapter 7. Find the P win in the game of craps. Repeat 10 times.