Archive for the ‘Probability’ Category

The Forgotten Hat

Saturday, October 27th, 2018

It was well known amongst his colleagues that professor Ambrose Helleborus would leave the house and later return without his hat, as a matter of fact, according to his housekeeper, Mrs. MacGillicuddy, this would regularly occur once after every four excursions on the town.

On a windy winter’s day, professor Ambrose Helleborus went to the university library to do some research on the legendary Kingdom of Agartha, after which he went to enjoy a tasty lunch at the Chez Antoine café, whereafter he spent a leisurely afternoon with cronies at the Jolly Hills Chess Club.

Subsequently, professor Ambrose Helleborus returned home without his hat, facing extensive interrogation by Mrs. MacGillicuddy, who would have to retrace his steps and retrieve the hat, as it was a treasured gift from professor Einstein.

But Mrs. MacGillicuddy didn’t mind as she by now had developed a circle of chat friends along professor Ambrose Helleborus’ usual excursion routes.

What are the respective probabilities that professor Ambrose Helleborus left his hat at the university library, Chez Antoine’s and the Jolly Hills Chess Club?

 

The Road Crossing

Tuesday, October 23rd, 2018

Seymore, a green frog, wanted to cross the road to get to his favorite pond where frog mates were plentiful. However, the road was a dangerous place to cross, and Seymore was worried he might get run over by a passing motor vehicle.

Brer Rabbit had told Seymore that on the average about a 100 cars would pass per hour along this stretch of road, which was valuable information indeed.

Seymore needed one minute to hop across the road and any car passing by could be fatal.

So he looked up at his lucky star and got ready to jump.

What would you say is the probability that no car would pass while Seymore was crossing the road and destroy his froggy dream to arrive at his favorite mating pond?

The Chess Match

Monday, October 22nd, 2018

One Sunday afternoon, a chess match was being held at the King’s Hills Chess Club where bets were being made on Henry MacDuff versus Melvin Longspur. Henry MacDuff was rated as a three times better player than Melvin Longspur.

Judge Roy Bean decided that they would play ten rounds and whoever won three consecutive times would win a copy of the famous Royal Diamond Chess set.

How many rounds would have to be played for Henry MacDuff to have a good chance of winning three consecutive games?

The Dice Club Project

Sunday, September 30th, 2018

One Saturday afternoon, as Jack, a new member, entered the Snake Eyes Dice Club he saw many people busy throwing dice at various felt-covered tables.

“Why are you repeatedly throwing that die, Vince, won’t you get a sore arm,” asked Jack.

“Hope not. I’m checking how many throws are needed to get all die faces from one to six to appear at least once,” said Vince.

“Any conclusion so far?” asked Jack.

“Seems that about 14 throws will do the job,” said Vince, after checking some marks on a notepad. “We’re running a project to check the results for different numbers of dice,” added Vince.

“So you’ll soon be using two dice to see how many throws are needed to get all the doubles?” said Jack.

“That’s the next step,” agreed Vince, “probably take quite a bit longer. Maybe I’ll pass the job on to Joe over there,” said Vince, rubbing his elbow.

“Charlie at the big table yonder is working on getting all the triples, but he’s been at it for a really long time,” said Vince.

“Anybody working out the probability for n dice?” said Jack.

“Yeah, my cousin Lennie at the desk over there is doing the theory and checking it out on a PC. He’s quite good at math,” said Vince.

“Good luck with the project, Vince. Seems a bit complicated to me, so I’ll be heading for the lounge,” said Jack.

Can you offer a formula for calculating the number of throws with n dice needed to get all the n-tuples?

 

Bags with Gold and Silver Coins

Saturday, September 29th, 2018

“Jack and Jill, which bag do you choose for a chance of winning ten thousand dollars,” hailed the cheerful game show host Dusty Farlone, “the blue bag with three gold and seven silver coins, or the red bag with four gold and three silver coins. What do you say?”

“Dusty, what were the conditions, again?” asked Jack.

“You can pick six coins out of the blue bag with ten coins, or you can pick six coins out of the red bag with seven coins, in both cases replacing the coin each time. Whichever bag you choose, if you manage to pick three gold coins, you will win ten thousand dollars plus all the coins in the bag, of course,” said Dusty Farlone, smoothing his slick hairdo.

“Our charming Marlene will bring you the bag you select so you can pick the six coins, and help you put them back into the bag again,” said Dusty Fallon, indicating the svelte Marlene. “You have a minute to decide while the music plays.”

Jack turned to Jill. “You took a course in probability theory. Which bag seems the most promising for winning the prize, Jill, the blue or the red one?”

“Hmm… good question,” said Jill, “quick, hand me your scientific calculator, Jack.”

Which bag would you say has the greatest probability of success for picking three gold coins and winning the game show prize of ten thousand dollars?

The Chinese Round Table

Friday, August 31st, 2018

One fine evening, Jack and Jill were dining at the Fu Manchu Magic Noodle House, their favorite Chinese restaurant. They sat at a round table served by their regular waitress, Wang Shu.

A number of dishes containing delicious tidbits for plucking off with their chopsticks were situated in front of them on a rotatable round tray.

Jack and Jill sampled the many delectable Chinese morsels to their heart’s content.

“Pick a fortune cookie, Jack,” said Jill, pointing at the decorated cookie jar in the center of the table.

“The cookie says: ‘Good fortune. Soon get special dessert’,” said Jack.

“Hmm,” said Jill, “what does it mean, Wang Shu?”

“Now, special desert,” announced Wang Shu while clearing up after dinner.

Wang Shu placed four dishes containing fried ice cream balls and spicy chocolate truffle balls – delicious Chinese desserts.

In each of the first three dishes there were two fried ice cream balls and eight spicy chocolate truffle balls. The fourth dish contained six fried ice cream balls and four spicy chocolate truffle balls.

“Fortune cookie offer special dessert,” said Wang Shu.

“How generous,” replied Jack.

“Bring it on, Wang Shu,” said Jill.

“Close eyes,” said Wang Shu, “you too,” addressing Jill. Wang Shu spun the dessert tray with the four dishes.

“Please, keep eyes closed and pick one dessert from dish,” said Wang Shu to Jack. Jack picked a dessert ball, which Wang Shu quickly replaced from a large pot containing both dessert types.

Jack opened his eyes and saw a fried ice cream ball melting in his hand, which he promptly ate to his great satisfaction.

“You guess which dish ball from, you no pay. Boss say special promotion,” informed Wang Shu.

“We like that,” said Jill.

Jack scratched his head and then wrote some figures on a napkin, Jill peeping on. Then Jack pointed to a dish.

“Correct dish you choose. Boss say, this time free, next time you pay plenty,” said Wang Shu with a big smile.

Jill was already busy munching away at the balls on the dessert dishes.

“Doggie bag, please,” said Jack.

Was Jack just lucky or had he worked out a probable dish to pick?

Which of the dishes do you think Jack chose?

The Flying Card

Tuesday, August 28th, 2018

At the Lucky Duck casino Nick, the dealer, was sitting at a green felt table and practicing fancy acrobatic shuffles with a deck of cards when suddenly one card flew away and sailed into a nearby plant bed with some petunias and foliage.

“I’ll bet ya 100 bucks you can’t figure out if da card dat just flew away from your deck is a red or a black one,” said Carmine, the floor overseer who happened to be walking by and observe the event.

“You’re on,” said Nick, “on one condition.”

“What’s dat,” replied Carmine with some suspicion.

“That I draw 13 cards from the deck at random,” said Nick.

“Ok, sure,” said Carmine, “no problem, Nick, go ahead an pull dem.”

Nick then drew 13 cards at random from the deck and they all turned out to be black cards.

Then Nick pulled out a calculator, a notepad and a pen and got busy making some calculations.

After some minutes had passed Nick proudly announced: “The card is red, Carmine, go and check it out.”

Carmine walked over to the flower bed and picked up a red card.

“Jeez, Nick, how did ya figger dat out?”

“Give me the 100 bucks and buy me a beer and I’ll tell you all about how to make a pretty sure bet,” said Nick.

 

Can you figure out how Nick knew that the card most likely was a red one?

The Faulty Die

Friday, August 24th, 2018

Jack was sitting at a café table reading a magazine when Jill sat down and ordered some pastries and a hot chocolate.

“What are you reading with such a puzzled look on your face,” said Jill, munching a delicious apple strudel with a flaky crust.

“It’s a puzzle about a guy who is given a bag with 100 dice and told that one of the dice is faulty since it has six dots marked on all of its faces,” said Jack. “Then he is told to reach into the bag and pick one die.”

“So what’s the puzzle all about, then?” asked Jill, taking a small sip of her hot chocolate.

“You’re supposed to work out how many sixes in a row the guy has to throw before he can be 90% sure that the die he is throwing is the faulty one,” said Jack.

“Hmm… since there are 100 dice, it seems to me that you’d have to throw an awful lot of sixes to be sure the die was faulty,” said Jill.

“Maybe,” said Jack, “but we have to give mathematical proof of the solution to the puzzle.”

“What’s the prize?” said Jill finishing off her apple strudel and taking a large sip of her not so hot chocolate.

“Jill, it’s ten thousand dollars for the correct answer,” said Jack.

“What are we waiting for, Jack!! Why don’t you get busy on figuring out the solution,” said Jill enthusiastically, “then we can rent an apartment in Mambo Bay for a great vacation.”

“Hmm…,” said Jack, “’Bay’ gives me an idea.”

Straight vs. Full House

Tuesday, August 14th, 2018

On another fine evening, there was a heated discussion at the Royal Flush Card Club as to how many occurrences of Full House and Straight would occur in the course of 30 throws of five poker dice.

Bing Jones III was betting $100 against Franz Fingerflitzer that he would get at least two instances of a Full House, the latter claiming at least two Straights during the trial – ties leading to a rematch until a winner emerged.

Lots of paper was expended and the whisky flowed freely while members of the Royal Flush Card Club busied themselves calculating the probabilities involved for throwing a Full House and a Straight.

However, accuracy and interest faded rapidly as whisky was poured, and this task was abandoned in favor of registering bets and proposing exuberant toasts, expectations rising to a high pitch, as if prior to a championship horse race.

Who do you think won the bet, Bing Jones III or Franz Fingerflitzer?

The Same Sun Sign

Tuesday, July 31st, 2018

“Jack, I’ll be taking a course in Astrology soon,” said Jill.

“That’s nice,” said Jack, “How many people will be on the course?”

“Twenty-five or so, I was told,” said Jill.

“How many people do you think will be Geminis, like you?” said Jack.

“No, idea. What would you say, Jack?”

Jack told her and it turned out he was pretty right.

What would you say was the number of other Geminis Jill met on the Astrology course?