A Cinderella Story: Revamped

Once upon a time, a long, long time ago, there was a girl named Cinderella. A beautiful, although quite aloof lady, Cinderella lived a miserable life. She resided with her stepsisters and stepmother in her deceased father's home, and was treated as a servant by her so-called "family".

She was required to do all the cooking, cleaning, laundry, of the house, and was not given a single penny for her efforts. Cinderella was sick of her sorry life and decided she needed an escape.

One fine morning, as Cinderella was waking up in her attic along with the mice and dust bunnies, she came to the conclusion that she had had enough. She was going to run away from home, and she was going to do it today.

Cinderella quickly got dressed, cooked herself a piece of burnt toast, and decided to run away from the house at that instant. She knew that she had to leave before any of her stepsisters or stepmother woke up.

Unfortunately, as Cinderella tried to escape from the window, she noticed that it was locked into place from the outside, and knew that her stepmother had done this to assure that Cinderella always stayed indoors.

But today, Cinderella did not want to give up. She noticed a lonely beige coloured rope sitting in the corner of the attic, and decided she'd use the rope as assistance to escape from the house.

Question 1: Cinderella is looking for a way to run away from home, away from her stepmother and stepsisters. She is testing out whether or not she should utilize a rope she found in the attic that has a 0.3 probability of damaging her hands, a 0.5 probability of breaking the bedroom window, and a 0.2 probability of damaging both. Determine the probability that the broken rope will damage her or her home.

Answer 1: A= damaging her hands

              B= breaking the bedroom window

P(A)=0.3

P(B)=0.5

P(A and B -both)= 0.1

P(A or B)= P(A)+P(B)-P(A and B)

               = 0.3+0.5-0.1

               = 0.7

The rope has a 70% chance of damaging Cinderella’s hands or her bedroom window. 

Because utilizing the rope had such a high probability of causing severe damages, Cinderella decided against it. She took a deep breath in and contemplated that potentially, someday in the future, the opportunity to run away from home would somehow present itself,

Cinderella went to downstairs to get ahead on making breakfast for her stepsisters, knowing that they would be screaming different orders at her any second by now. But, to her surprise, as she went to the kitchen, she saw a small note with her name on it. The note said, "Cinderella, we are going to a fundraiser to find ourselves a prince. Don't make breakfast, but make sure you have a lunch prepared for us at noon sharp."

Despite her circumstances, Cinderella chuckled. A prince! Imagine! What girl in her right mind dreams of marrying a PRINCE? Such a dream that is never to happen? Crazy!" Cinderella thought to herself.

Question 2: Cinderella’s stepsisters are at a fundraiser where they can find an ideal prince/duke/businessman of their choice. There are 15 dates in total that can be won.Winners of the fundraiser are given 2 dates with a prince, or 4 dates with a duke, or 9 dates with a businessman. Cinderella’s stepsister Fiona really wants a date with a prince or a duke, but definitely not a businessman. Assuming Fiona wins the fundraiser, what is the probability she will get to go on a date of her liking?

Answer 2: P=Prince                                    P(P or D)= P(P)+P(D)

D=Duke                                                     = 2/15+4/15

                                                                   =6/15

                                                                    =2/ 5

Fiona has a 40% probability of going on a date of her liking.

A couple of hours later, one of Cinderella's stepsister's, Fiona, comes into the house with a gleam in her eyes. She screams, "GUYS! Guess who went on a date with the prince's younger brother? Me!"

Cinderella, who was busy wiping off dust from the living room table, brushes a strand of hair from her forehead and sighs. She could never imagine going outside on a date with anyone, let alone a prince.

Cinderella's stepmother walks into the living room and sits down, Fiona and Amy by her side. "And, he even told me that his parents are planning on organizing this major ball, and that we'd be invited, of course. Apparently, this ball will be set to announce the future King of France too!" Amy shrieks in happiness, and her and Fiona jump up and down excitedly. The stepmother smiles quietly, then turns to look at a smiling Cinderella. "Now, now, Cinderella. You needn't be smiling right now. You are not invited. It is JUST our family. Understand? Now go finish the rest of the chores," the stepmother says, her face in a scowl. Cinderella quickly nods, and leaves the living room as fast as possible, tears flowing in her eyes. As she is about to head into the balcony, she hears Fiona say, "The issue is, the King and Queen don't exactly know when to host the ball. It's always raining in France, so they have to decide very carefully, you know." Cindrella wipes her eyes and shrugs. Who wants to go to a rainy ballroom dance anyway?

Question 3: Before organizing the date of the ball, the Queen and King check the weather to make sure it is not raining on the day chosen. They decide to have the ball on Friday. On that day, the probability that it will be both cloudy and rainy is 15%. Furthermore, 60% of all days in France are cloudy. Determine the probability that it will rain during the ballroom dance day given that it is cloudy. Did the King and Queen make a wise decision on hosting the dance on that day?

Answer 3: Let A= cloudy

      B= rain

P(A and B)= 0.15

P(A)= 0.6

P (B I A)= ?

P (B I A)= P(A and B)/P(A)

              = 0.15/0.6

              = 0.25

There is a 25% chance it will rain on Friday given that it is cloudy. This is an unlikely probability, so the King and Queen did make a wise decision.

Although Cinderella busies herself with household work, she cannot get the nagging feeling of wanting to go to the ball out of her head.

The night of the ball, Cinderella assists in getting Fiona and Amy ready. She brushes their hair, irons their dresses, and powders their faces with blush and perfume. She buttons her stepmother's gown, and polishes their shoes, too. A few hours later, the stepsisters believe they look adequate enough, and leave to head to the ball. The s tepmother glares at Cinderella. "We will back early morning tomorrow. Make sure to have our beds made and breakfast ready. And, do not go anywhere. Understood?"

Cinderella nods her head meekly, and closes the door as her stepmother heads out, the sisters following close behind.

Once Cinderella has completed all her tasks, she heads to the balcony and stares at the moonlight shining on the railing. She looks up at the stars and begins to feel very sad. She begins missing her father, her mother, and the way life used to be.

Slowly, tears start creeping up in Cinderella's eyes, and eventually, she starts to wail. Suddenly, she feels a tap on her shoulder and gasps."Dear girl, you know crying won't fix anything, right?" a woman says. The woman is wearing a dark green robe, and is carrying a wand. She seems to be looking... magical."W-who are you? How did you get inside?"

Cinderella says, scared.

"Us magical beings don't need to knock on doors to come inside. Ha! It was a joke. Sorry. Anyway, I am your fairy godmother!" the woman says, laughing.

"My who?" Cinderella asks, her brows furrowed.

"Think of me as your guardian of sorts. I'm here to fulfill a wish of yours, to make you a little happier. Now, wouldn't you like that?" the woman says, sitting next to Cinderella and touching her shoulder.

Cinderella could not believe her luck. She stood up as fast as lightning and tightly hugged the fairy.

"Thank you," Cinderella said earnestly.

"Now, come on. It's time for the ball, and you my dear, are going to be the prettiest girl there.

The godmother dresses Cinderella in a beautiful blue gown, and magically turns the mice into pumpkin carriages. She then hands Cinderella a pair of glass slippers and tells her to wear them during the ball. Cinderella laughs with joy and thanks the fairy constantly.

"Darling, I need you to listen to me carefully. You look stunning, and I know it can be very easy to get caught up in a ballroom party and dance the whole night away. But my powers are limited. You must return home as soon as midnight hits, otherwise your clothes will turn into rags, the carriages back into mice."

Cinderella nods understandably and promises to return before midnight. The fairy godmother gives her one last smile, then disappears into the darkness.