Archive for the ‘Probability’ Category

The Winning Seats

Thursday, June 28th, 2018

The McDuffy Travel Agency was offering special prizes for vacationers to improve its turnover. The advertising stated that the prizes would be determined on the airport bus.

One day there were fifteen vacationers going to the Caribbean island of Buena Siesta for a two week holiday at the Balmy Breezes Beach Resort. Before boarding the airport bus, which seated twenty persons, they were addressed by their charming tour guide Melanie Goodbottom.

“Two of you could win some awesome prizes if you are lucky enough to sit in the two seats with pre-determined prize seat numbers,” explained Melanie Goodbottom waving a clipboard with the passenger list at the entrance to the airport bus, skirt flapping in the wind.

“The winners will receive a week of free dinners for two at any of the best restaurants in Morgan Town, their choice of sightseeing tours for two all over the island and/or scuba diving lessons for two – for those of you who are of the sporty type, of course,” said Melanie Goodbottom enthusiastically, brushing some windblown locks out of her eyes.

The vacationers eagerly thronged towards the airport bus door, climbing over each other to mount the steps of the bus. Those who entered scurried to seat themselves at random, leaving five seats unoccupied for staff.

The bus driver grunted, sitting down at the wheel, and the porter got busy loading luggage into the lower compartments of the airport bus, while Melanie Goodbottom helped pull a number of the more portly passengers up the steps leading to the seating level of the bus.

When all the passengers were finally settled into their lush seats eagerly anticipating the results, Melanie Goodbottom picked up a microphone to announce any winners via the loudspeaker system, and the bus driver switched gears to get the show rolling towards the airport.

What would you say is the probability of two passengers winning these prizes?

 

The Broken Glasses

Friday, March 30th, 2018

At Danny’s Beach Bar run by Danny McDoogle at a popular Andalusian beach, there were five waiters who would take turns washing glasses used by customers.

One day there were five broken glasses, four of them caused by one of the waiters named Pedro.

Danny McDoogle was furious, figuring that this was certainly beyond the realms of chance and due to sabotage. So, he decided to fire Pedro for damaging his property.

The other waiters stood up for Pedro claiming that this could happen to anyone.

Based on probability, would this event be a valid reason to fire Pete for being careless, or could it have been an accidental occurrence as the waiters claimed?

The Twin Birth Rate

Monday, February 26th, 2018

“Did you know that seven pairs of twins are born on average at each of the hospitals in Brownville?” said security guard Barney Coxworth to Hank Burnside, the janitor of the Belleview Hospital.

“Naw, had no idea, Barney. Why is that important?” said Hank, steering his mop bucket into a corner to listen further.

“Well, Hank, I’ll bet you 100 dollars that during the coming month there will be no week at any of the five hospitals in Brownville during which twins are born consecutively on each day of any week,” said Barney.

“Barney, if seven pairs of twins are born every week at each of the five hospitals in Brownville, I figure the stork might just decide to arrive every day now and then.”

“Right you are, Hank.”

“Only makes common sense, Barney,” said Hank,“ so I’ll take you up on your bet.

“With a hundred dollars I could buy a pair of shoes,” said Hank.

“Ok, let’s spit and shake on it and see how it goes, Hank,” said Barney with a poker face.

I wonder who you think will win the bet, and why?

The Dance Academy

Friday, November 17th, 2017

Jean-Pierre was walking down the Rue de la Bonne Chance in Paris one early spring evening when through a large display window he saw many couples dancing in what appeared to be a softly lit dance academy, and noticed the graceful movements of a beautiful young woman.

Jean-Pierre instantly fell in love and walked through a door above which a large, blinking neon-lit sign read: “Chez Antoine de le Boeuf École de Danse” to speak with a registrar.

Jacqueline, the registrar, explained that for each dance lesson ten male students would be lined up at random to face ten female students arranged in a line at random.

The instructor, Madame le Coeur, would push a button on a hand calculator with her long, red fingernail to generate a ten digit number each time a line of students had to be arranged, the students lining up according to their own number.

The eager Jean-Pierre was told he could buy various packages, such as for 7, 14, 21 or 28 lessons.

Jean-Pierre tried to work out how many lessons he would need to be 50% sure of being paired with the enticing woman, he found out was called Emmanuelle, for a dancing session.

Jean-Pierre figured that if the first session package did not work out, he could always buy some more packages.

Which lesson package would you suggest Jean-Pierre should buy to be able to dance with Emmanuelle with a certainty of 50%?

If the first package didn’t work, how many more packages should Jean-Pierre buy to achieve a success rate of 90%?

The Christmas Gifts

Thursday, August 31st, 2017

Fred and Mary were trying to work out how to give five gifts to their three boys for Christmas.

The kids, Henry, Mark and Joe, had told them they wanted to receive gifts more or less at random this year to see how the gifts would be distributed.

“We have five gifts to give to three children. How are we going to do this, Mary? There are so many possibilities it makes my brain spin,” said Fred in exasperation.

“Well, Fred, we have to make sure they all get at least one gift, so that makes it easier than the way you are thinking of, doesn’t it,” Mary said reassuringly.

“You’re right, Mary. The number of ways of giving the gifts so that our kids might not receive even one gift is quite large,” said Fred.

“Do it my way and the matter becomes more simple,” said Mary.

So Mary and Fred distributed the gifts as she suggested.

If they distributed the gifts Fred’s way what would be the probability that one or more of the kids received no gift?

The Die Game

Thursday, August 24th, 2017

Jerry and Slick were sitting at a bar drinking beer and watching a championship football game being televised on the huge wall screen, a bowl of peanuts close at hand.

“Hey Jerry, want to play a game?” said Slick, taking a large sip of his cold beer.

“Sure, what’s it all about,” replied Jerry, munching on some peanuts while eyeing the curvy waitress.

“It’s really simple. I throw this die and if you throw a higher number, you win one point, otherwise I get the point,” explained Slick as he placed a large red die between the beer glasses on the green felt-covered bar counter.

“Let’s try it first, Slick,” said Jerry with a suspicious look.

Slick threw the red die and got a two. Then Jerry threw and got a three.

“Hmm, seems like a good game,” said Jerry with a sly smile.

“Glad you like it, Jerry. How about we play twenty rounds, or until the football game is over – point loser pays the bill?” said Slick.

“Fine by me,” replied Jerry, giving a loud cheer for a goal just made and snatching a handful of peanuts from the bowl.

Slick ordered some fast food and they rolled the die until the end of the football game.

Who do you figure paid the bill, and why?

The Speedy Pigeon

Friday, June 30th, 2017

“Hurry, hurry, try your luck, folks. Get lucky and win a thousand dollars with one shot,” shouted the hawker at full lung power to announce the new game stand at the Jolly Woods Amusement Park.

People flocked to the stand in droves to learn more about this intriguing new game. When they arrived they saw a large semicircular amphitheater with a huge screen about 50 m away facing the spectators. The setup reminded them of a drive-in movie theater of old.

They were told that a yellow virtual pigeon with a blinking red light would be shot out on the screen at a very high speed, leaving a trail of light. To win a thousand dollars a player had to hit the pigeon using a special laser gun each seat was equipped with.

One shot cost $10 and players were told that the chance of hitting the speedy virtual pigeon was 4 in a thousand. Payment was via a card slot at each seat, wins immediately transferred to the card.

Another feature was that for $500 a player could once invite up to two hundred friends to simultaneously take a shot at the pigeon for free.

“C’mon Charlie, lets give it a shot,” shouted one burly onlooker, taking a seat and picking up the laser gun.

How many friends would you invite to this game to have a fifty percent chance of hitting the virtual speedy pigeon and winning five hundred dollars?

The Elevator

Thursday, May 11th, 2017

At the hotel Excelsior, Melvyn had stopped by the security office run by his friend Zack. They were watching the elevator on the split screen monitor, with one screen for each of the ten floors of the hotel and the ground floor.

“Zack, you see the seven people entering the elevator on the ground floor?”

“Sure, Melvyn, especially that hot blonde that just wiggled in before the door closed,” said Zack, chewing on his bubble gum.

“Zack, I’ll bet you a hundred bucks that there will not be a group of exactly three people getting off the elevator at any floor,” said Melvyn.

“You’re on, I could really use a hundred bucks,” chuckled Zack.

“Are you really sure that three persons will be getting off at some floor?” quieried Melvyn, raising an eyebrow.

“That’s what I’m betting on, Melvyn.”

“Well, let’s see how it goes, Zack.” Melvyn made himself comfortable in an armchair to watch the monitor.

What do you figure are the chances that Melvyn will win his bet with Zack?

Can you work out the probability that only one person gets off the elevator at each stop?

The Four Aces

Sunday, April 30th, 2017

Fred was playing poker with his three friends Henry, John and Mack and had just dealt a hand for each.

Fred saw that he had an Ace and wondered what the probability was that each of the other players also had an Ace.

Later in the evening after the game, Fred decided to write a computer program that would deal ten thousand hands of poker to check how often four players each would be dealt an Ace.

Then Fred wondered what would be the similar case for bridge hands dealt, for which purpose he changed a few input parameters for his computer program and received a surprise answer.

On the average, how many of the ten thousand poker hand deals do you think resulted in an Ace for each player?

On the average, how many bridge hand deals did Fred find gave an Ace to each player?

An Olympic Swimming Team

Monday, April 10th, 2017

Jack is part of a ten member Olympic swimming team.

A 500 m relay race is to be run with five contestants.

What is the probability that Jack will be among the five contestants chosen?