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Counting Stories Project
Transcript of Counting Stories Project
One day, the palace gets a visit from the Paige of a far away kingdom. He carries an invitation to an upcoming ball, where the Prince of the kingdom will be choosing a princess to marry. How many paths can the Paige take to get to the palace? Cinderella's step mom says that she can't go to the ball unless she does her chores. There are 30 chores on the list. Cinderella flips a coin 30 times. Each time she gets heads, she must do a chore. What is P(1/2) chores done meaning she does the half of the chores which is (15) P(30 or H)
= P ( 30)+ P(H) -P(30 & H)
= 2/30 + 30-30-15/30
=17/30 Cinderella knows it is physically impossible to complete all the chores before the ball, but she begins to work on them regardless Cindy has X chores to do , she must do Y chores first , in how many arrangements can the chores be done? Cindy has 35 chores and she has to do at least 25 chores.
P= 35 P 25
= 2.847538571 x 106^35 Cinderella’s stepmother demands a dinner of her choice. Cinderella must prepare a main course, a side, and dessert. Cinderella is trying to think of the fastest meal she can make so that she can get those chores done. 2 main courses: Beef, Chicken4 sides: Soup, Salad, Baked Potato, or Bread3 deserts: Cake, Ice Cream, or Fruits
Fastest meal: chicken, bread or salad, and ice cream or fruits
1/2 x 2/4 x 2/3
Chicken Bread Ice Cream
1/6 times Cinderella will be able to prepare a fast meal for her step mother. Using a pumpkin and seven mice, the fairy creates a beautiful horse carriage for Cinderella to go to the ball in. “Have fun, princess! But make sure you are home by midnight – as that is when the magic will wear off!” There are 12 dresses. 3 blue, 5 pink, 2 white, 2 yellow.
What are the odds in favour of cindy picking a blue dress?
3/12 ÷ 9/12
= 1:3 There are 23 mice in total, there are 17 large mice and 6 small mice. The larger mice are able to wash the dishes and the smaller mice will dust the house. The fairy got mother only needs 6 mice to wash the dishes and at least 2 mice dusting the house. How many groups of helpers can be made? 17C6 x [6C2 + 6C3 + 6C4 + 6C5 + 6C6]
= 705, 432 Cinderella goes to the Ball! If there are 27 Jazz songs and 12 pop songs only being played randomly, In how many ways could Cinderella get to dance to either 5 Jazz or 5 pop songs?
1st Case: Choosing 5 Jazz songs- 27c5
2nd Case: Choosing 5 Pop songs- 12c5
Ways of choosing either 5 Jazz or 5 Pop songs= 27c5 + 12c5 = 80730 + 792
= 81522 ways Looking for the Prince Cinderella wants to know how many princes are wearing Tie, Waist Coat and Glasses?
A) Tie: 18
B) Waist Coat: 12
C) Glasses: 15
P(AuBuC)= P(A) + P(B) + P(C) - P(AnB) - P(AnC) - P(BnC) + P(AnBnC)
So, Number of princes wearing everything is 24. Out of 50 princes, Cinderella chooses 9 randomly to dance. But out of them there are 2 twin brothers, In how many ways can Cinderella dance with 11 of them without having to dance with twins consecutively? Total Princes: 9
Total number of ways: 9!/ 2!.2!
362880 ways The first chime of midnight strikes, and Cinderella runs away from the ball. In the haste of getting home on time, her glass slipper falls off at the door. The prince chases after her to return it, but Cinderella has no time to waste. There is a 15% chance of Cinderella losing her slipper while running out of the palace. The chances of her getting home late – considering the time she left – are 60%. What is the probability of her losing the glass slipper AND getting home late? Cinderella is luckily home on time, saving suspicion from the stepmom. Meanwhile on the other side of the city, Prince Charming is restless and wants to find his lady from the ball. He goes on a hunt to find the Princess who lost her glass slipper. The prince has 26 maps – one for each of the different palaces of the Royal city. Each map is ripped into 2 parts. What is the probability that the first map the prince chooses is for Cinderella’s palace? What is the probability that the second map he chooses matches the first? Finally, the Prince appears at Cinderella’s palace. Her stepsisters Anastasia and Drizella run to him and try to fit into the glass slipper. Their attempts fail, as the Prince notices Cinderella peeking from the door. Sparks fly, and he knows she is the one. He insists that she tries on the slipper, but her stepmom questions his reasoning. Eventually, the slipper does fit, and the Prince takes Cinderella into his arms and kisses her. *Do not assume that if Cinderella is late, it is BECAUSE she lost her slipper. These two are independent events, where their outcomes are not differed by the other.
Let x represent Cinderella losing her slipper P(x) = 0.15
Let y represent Cinderella getting home late P(y) = 0.6
P(x and y) = 0.15 * 0.6
= 9% 26 maps in 2 pieces each = 52 total pieces
Let A represent the first half of Cinderella’s map P(A) = 2/52
Let B represent the second half of Cinderella’s map P(B|A) = 1/51 P(A and B) = P(A) * P(B|A)
= 2/52 * 1/51
= 1/1326 Therefore, the chances of the Prince choosing both halves of Cinderella’s map within the first two attempts is approximately 0.075%, which is not very likely. He will have to try multiple times before arriving at his desired destination. Along with the fitting shoe, prince charming brings Cinderella jewellery as a gift. He has 5 necklaces and 8 bracelets. He tells Cinderella to pick 3 of her favorites. Cinderella loves them all, and decides to pick the 3 at random. What are the chances that all 3 of her choices will be necklaces or all 3 will be bracelets? 5 + 8 = 13 total items
Let A represent necklaces
Let B represent bracelets
P(A) = 5c3/13c3
P(B) = 8c3/13c3
= 56/286 P(A or B) = P(A) + P(B)
= 10/286 + 56/286
= 0.23 Therefore, the chances of Cinderella choosing all 3 necklaces or all 3 bracelets is 23%, which is very rare. She will most likely choose an assortment of both kinds of jewellery. Anastasia, Drizella, and the stepmom are in shock. They watch the Prince carry Cinderella away in his arms, who both live happily ever after. THE END Shrushti - Pascal's Triangle Shrushti - Theoretical Probability Shrushti - Permutations (Non-identical items) Sharan - Tree diagram Sharan - Odds Sharan - Combinations (some unique items) Kamal - Experimental Probability Kamal - Combinations (exactly r items) Kamal Khadija - Independent events Khadija - Dependent events Khadija - Mutually exclusive events Therefore, the probability of Cinderella losing her slipper and getting home late is 9%. Although Cinderella did lose her slipper, she was luckily home on time.Therefore, the probability of Cinderella losing her slipper and getting home late is 9%. Although Cinderella did lose her slipper, she was luckily home on time.