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It’s Carnival Time!

It’s Carnival Time! . Kyra Barrett, Destiny Hopkins and Gaby Orellana .

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It’s Carnival Time!

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  1. It’s Carnival Time! Kyra Barrett, Destiny Hopkins and Gaby Orellana

  2. This is Tommy. Tommy’s First Grade class are heading to their school carnival today. Tommy is extra nervous about the carnival because he wants to win King of the Carnival, but is afraid he won’t because he is so small. Will you believe that Tommy can win the most games and be King of the Carnival even though he is so small?

  3. Everyone decides it’s a good idea to fuel up at the hotdog stand before they start playing games. The Math: Each person can choose 1 sauce and 1 topping to put on their free hotdog. Order does not matter. 12 C 3 = 220 Combinations At the Hot Dog Stand: You can choose between (3) Sauces Ketchup, Mustard and Cheese (4) Toppings Tomatoes, Pickles, Onions, Sauerkraut Tommy gets a hotdog with Ketchup and pickles and then goes to the card draw. Combinations

  4. At the Card Draw: Tommy notices that there are 52 cards in a standard deck. At Card Draw Tommy must pull one of the Aces from the deck on his first try to win a prize and be one step closer to being King of the Carnival. The Math: There are 52 cards in a standard deck 4 Aces Because you can not draw more than one card at a time the probability of drawing an ace is 4/52 4/52 = .076% On his first try Tommy selects a Red Ace, he receives one point toward being King of the Carnival and then heads toward the color wheel. • Mutually Exclusive

  5. Green Red Blue • yellow Red Red At the (more official looking) Color Wheel: Tommy has to spin a yellow on the color wheel to win a prize and a point toward becoming King of the Carnival. He then headed towards the Ring Toss. Green Blue Unfortunately Tommy spun a blue and did not win a prize or a point toward becoming King of the Fair, and next goes to the Best of Luck Booth. The Math: Because of the uneven amount of coloring the probability of spinning on yellow should be 1/8 (Classical) However, after the day at the carnival and totaling the spins the probability was 1/16 (Empirical) Classical vs Empirical

  6. Tommy did not win a prize at the Best of Luck booth or receive a point towards being King of the Carnival and next headed to the balloon pop. At the Best of Luck Booth: In order for Tommy to win he draw an ace, any ace from the deck of cards and flip heads on the quarter. The Math: Independent Event: There is a 4/52 (1/13) chance Tommy will draw an ace, and ½ chance that Tommy will flip the quarter and it will land on heads. Neither of the events will influence each other. Dependent Event: If Tommy were to draw two cards from a deck of 52 cards. On his first draw he had an ace and put that aside, the probability of drawing an ace on the second draw is greatly changed because he drew an ace the first time. >>> 4/52 (first time) 4/52- 1/1 = 3/51 chance. Independent vs Dependent

  7. Key : O= unpopped balloon X= popped balloon Balloon Pop At the balloon pop Tommy must hit at least 3 balloons to win a prize and a point toward becoming King of the Carnival. However, as the day has gone down of the 25 balloons the game started with some have been popped, and some have not. The Math: Because 10 of the balloons have already been popped Tommy only has 13 opportunities to hit, and he has to hit three times. 13/25 (3) = 39/75 X O O O X O X O O X X O O X X O X O O X Tommy did hit 3 balloons, received a prize and another point to go towards becoming King of the Carnival. X X O O O Conditional Probability

  8. At Ring Toss: Tommy is a small boy, he doesn’t have much power behind him that is required for this game. Tommy must stand behind a line and toss rings at bottles. To win he must get 3 rings around 3 bottles. The Math: As mentioned before Tommy is very small. Because he doesn’t have that much power he is expected to have a 1/25 chance to make 3 rings around 3 bottles. 1/25 x 1/25 1/25 = 1/15625 chance Tommy did not beat his odds at ring toss. Ring toss was the last game at the Carnival. Now, with the rest of his class, he waits at the awards table to find out the King, Queen and Court Jester of the Carnival Fundamental Counting Principle

  9. The King, The Queen and The Court Jester of the Carnival Prizes and points are all that kids care about at a carnival. Tommy is no different. All kids in Tommy’s class (25) spent the day at he fair competing and earning points towards their awards. King = First Place Queen = Second Place Court Jester = Third Place Because order does matter we have to use Permutations 25 P 3 25 P 3 = 13, 800 combinations Unfortunately Tommy didn’t win King of the Carnival this year, but there is always better luck next year! Permutations

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