Ken's blog

Sally Jones arrived at the Mega Market Mall and slid her white Ford Fiesta in among eight other cars in a parking section that could accommodate nine.

Sally received a call from Molly while parking.

“I’m at a restaurant right now lunching with Jane, Sally, but we’ll soon be off to the Mega Market Mall in separate cars,” said Molly excitedly. “There’s a big sale on shoes. How can we meet up?”

“Just park your cars on both sides of my white Ford Fiesta. I’ll be able to see you between the trees from the window of the art exhibition hall, and I’ll come get you.”

“But if the slots next to your car are occupied, how can we meet?”

“There is lots of traffic in and out of the mall. Should be no problem.”

Molly didn’t seem convinced.

If there were five cars including Sally’s in the parking section, what would be the probability that Molly and Jane could park alongside Sally’s car?

On a Saturday evening early in May, there was a televised live band Latin dance show with ten selected couples gyrating at the Mundo de Salsa Dance Hall.

“Welcome to the Buenavista Travel Agency promotional dance, amigos. At the end of the evening some of you may become the winners of a world tour, all expenses paid,” announced Carlos Sanchez, the host, in a promising tone of voice.

“Jill, this is a great party,” said Jack, stepping rapidly to the salsa rhythms. “Let’s see about winning the prize at the end of the evening.”

“That’s probably why we are each wearing a number, Jack. Love this kind of dancing,” said Jill, gyrating her hips and twisting her body to the captivating music.

Later, at the end of the evening, after a loud fanfare from the band, Carlos Sanchez took up the microphone again.

“Buenos amigos, we have arrived at the magic moment of selecting the winners of the world tour. Soon eight random numbers will appear on this screen,” said Carlos Sanchez, indicating a display suspended from the ceiling above him.

Jack and Jill fixed their attention on the display.

“If the number you are wearing appears, please sit at the table here to my left,” said Carlos Sanchez, indicating a small, round table nearby.

Jill moved closer to the table.

“Should you then also see your partner sitting at the table, you will both have won a world tour,” said Carlos Sanchez.

”I’m sure we’ll win,” said Jill animatedly, “I’ve already bought a new travel case.”

What would you say is the probability that Jack and Jill win a world tour?

What about the probability that at least one couple wins?

And what is the probability that exactly one couple wins a world tour?

“Welcome to a special promotional event sponsored by ACME Innovations Inc.,” said PR Jane Doe, speaking enthusiastically into a microphone to a hundred guests gathered in a large salon.

“ACME Innovation Inc. has developed a special velcro sticker which has been designed to test the spreading of rumors. It displays a number on a small LCD screen. By reading a persons’ unique vitality field, the number is incremented by one on being handed to someone else,” explained Jane Doe pleasantly.

“When you receive it, please pass on the sticker someone nearby. I’ll be mingling with you all and when the badge returns to me by this process of random handovers, whoever in advance has correctly guessed the number that will be displayed on the badge will win a thousand dollars,” said Jane Doe.

“Please enter you name and the number you estimate or guess on a slip of paper that you will find on the table over there by the entrance and place it in the box,” said Jane Doe, indicating the table.

Jane Doe stuck the velcro sticker on the first person nearby, and the procedure begun.

What is your estimate of the most probable number on the badge when it is returned by a random path to Jane Doe?

“I wonder where the entrance to the sub cellar is?” said Dr. Arbuthnot Smythe, looking around the vast basement.

“What a beautiful statue of Venus, look there between the two pillars at the far end wall,” exclaimed Dr. Smythe, as his assistant Pascal’s flashlight illuminated it briefly.

“Really impressive, Dr. Smythe. The room is full of statues and artworks, but I see no trap door anywhere,” said Pascal, continuing to search the poorly lit space with his flashlight.

“Wagner T. Buckfuller’s granddaughter, Isabel, said his will indicates that her inheritance is located in a sub cellar with access through a trap door,” said Dr. Smythe.

“Wait, I see a tablet on the wall over there with some writing,” shouted Pascal, running over to a far wall.

Dr. Arbuthnot Smythe quickly followed to have a look at the tablet hanging in a blue frame.

“It seems like gibberish, said Dr. Smythe, “must be a code.”

Pascal pulled out a notebook, “Let me have it, Dr. Smythe.”

“TPNTT-HUIRE-ESPAA-SHPPT-TVLDT-AEEOO-TNAOO

-UUNRP-ESPUE-BLTNN-AEUDT-SFREH-ETNRE”

“That really is a mouthful,” exclaimed Pascal.

“Columnar code with a keyword, obviously,” replied Dr. Smythe.

“I wonder what the keyword could be, some particular fondness of Wagner T. Buckfuller’s?” said Pascal.

“When we discover it, the task will be an easy one,” said Dr. Smythe.

“Let’s have a chat with Isabel. Knowing her grandfather’s idiosyncrasies, perhaps she can give us a clue.”

Can you work out what the coded tablet text says in order to help Dr. Smythe and Pascal locate Isabel’s inheritance?

“Looks pretty suspicious to me, Molly,” growled Sam Diamond, peering out of the window at the parking lot below through two slats he held apart in the blinds.

“What do you mean, suspicious?” asked Molly with a worried tone. She stood up to join Sam at the window.

“Don’t you see those cars over there in the shadow area of the street light?” said Sam, adjusting the pistol in the holster hanging inside his jacket.

“I see some black cars,” said Molly, “but what’s so suspicious about them?” Molly wasn’t gifted with a  great deal of imagination.

“The way they’re parked, of course,” snarled Sam, peering more closely with his nose touching the window pane.

“I just see nine black cars parked side by side in a zone with white stripe marks in the street for 14 cars,” said Molly, “and what’s so suspicious about that?”

“So why are they all parked together with the other five spaces empty, eh?” said Sam, “I tell you, Molly, something funny’s going on.”

Sam pulled out his gun and left the office to go investigate, and Molly sat down, blonde curls dangling over her bewildered face.

Do you think Sam had any reason to be suspicious on seeing the arrangement of nine cars parked side by side in a small parking zone intended for fourteen cars, considering the probability of such a configuration?

One rainy Saturday evening some years ago in lower Manhattan, Jane, a ticket girl, rushed into the  booth of the Roxy movie theatre to prepare things for the night shift.

As usual, Eusebio, the evening shift ticket seller, had left the booth in a mess, with an ashtray full of thin butts, and Jane was shocked to see the cash register empty – no bills to give change with.

Jane looked up to see some Japanese tourists lining up to buy tickets for the five-dollar late movie of the evening “The Seven Samurai”, when a toothy, smiling and bowing Japanese who seemed to be the tour guide stuck his face in into the ticket window.

“Kon’nichiwa, me Mr. Fujimori. We ten tourist from Osaka, see samurai movie. Half have 10 dollar bill, other half have five dollar bill. You give change, buy ticket, no problem, ok?”

“Sure, Mr. Fujimori, I’ll do what I can to give you all correct change,” said Jane politely, feeling a mounting panic, knowing that the cashbox was empty.

“What shall I do, what shall I do…” spun around in her head, “What if the first person to buy a ticket gives me a ten dollar bill? I won’t have any change to give back.”

Then Jane got a bright idea, which she implemented with the aid of Mr. Fujimori, and all tickets were sold with correct change given so that Jane ended up with fifty dollars in the till.

What would you say was the bright idea Jane got to solve this problem?

What would be the probability of successfully terminating each ticket transaction without any problems giving change if the Japanese in the queue had been lined up at random?

Lenny was out on the town with his daddy and they entered a toy store.

“I would like to buy twelve marbles, daddy,” said Lenny loudly.

“Ok, my boy, let’s ask the man,” said daddy.

“We have lots of marbles, sonny,” said the shopkeeper, smiling down at the young boy, “and they come in five different colors.”

“That’s really wonderful, mister. Do you know how many bags with different combinations of twelve marbles with these five colors you could sell?” asked Lenny, cocking his head with an impish look on his face.

“No idea, sonny, but if you tell me you can have your marble order for free,” smiled the shopkeeper.

Lenny told the shopkeeper, who believed him, and Lenny happily skipped out of the store with daddy, holding three bags of marbles in his hand.

How many different bags of marbles would you say the shopkeeper could arrange for sale?

One Sunday evening in River City, CNXY was in the process of televising a mayoral candidate debate with ten aspirants so they could practice their persuasive oratory on voters to gain their votes.

A random method was employed to program the speaker sequence, but it had been secretly pre-arranged by concerned citizens that Barnard S. Fagg would speak before Sheldon M. Weeder.

However, since Corby, the programmer of the random method, was somewhat inexperienced, he couldn’t guarantee whether Barnard S. Fagg would speak immediately before Sheldon M. Weeder, or there would be an interval of several speakers after Barnard S. Fagg.

Sheldon M. Weeder’s campaign manager considered it vital that Weeder should speak immediately after Barnard S. Fagg so that the plethora of flowery utopian statements expounded by Barnard S. Fagg could be disproved and ridiculed – a task which Sheldon M. Weeder was an expert at accomplishing.

At the CNXY television station, the mayoral candidates were then placed in seats around a table on the platform in the programmed order, and were all preparing to ply their persuasive abilities on the TV public so as to secure their votes in the coming mayoral election.

What would you say was the probability that Barnard S. Fagg would speak immediately before Sheldon M. Weeder so the latter could accomplish his task?

Jake, now a full club member, was back again at the Happy Valley Card Club on a cold and snowy Friday evening.

As usual, there were many people standing around a large rectangular table by the bar, where Charlie, the dealer, was busy having someone pick a card from a pack on the green surface.

“What’s the game this evening, Charlie?” asked Jake, rubbing his cold hands together.

“Well, Jake, you pick a card from the deck. If you get a high card you pay me ten dollars, otherwise you win as many dollars as there are pips on the card,” said Charlie.

“By high card I assume you mean a Jack, Queen, King or Ace?”

“You got it,” said Charlie, “wanna play?”

“Ten dollars seems a bit much, Charlie, but I’ll give it a try to see how it goes,” said Jake.

“Suit yourself,” said Charlie.

After ten games, how much would you say Jake won or lost on average?

Jake dropped by the Happy Valley Card Club to see what was happening on a snowy winter’s Friday evening in December. Jake enjoyed the conviviality and high-spirited discussions about the probabilities of card games in the lounge by the bar.

Jake saw a large gathering around a large rectangular table, where Charlie was dealing cards on the luxurious green felt cover, Christmas music sounding enchantingly in the background.

“What’s the game this evening, Charlie?” asked Jake.

“It’s a variation of the game of the other day. It is called the ‘Four Card Deal’,” said Charlie. Half of your winnings will go to our university scholarship Christmas charity.

“Sounds fine to me. How does this ‘Four Card Deal’ work,” said Jake.

“Well, my man, you pay me 10 dollars and I shuffle and deal four cards face up. I also pull a card from the top of a stationary deck I don’t shuffle,” explained Charlie.

“Very interesting, but what’s the idea?” said Jake.

“If the four cards all have a different suit and no two the same value, you win. But if I pull an ace from the other deck, you lose,” explained Charlie.

“What’s the prize?” asked Jake.

“You win twenty dollars, but if you don’t win and I pull no ace, I repeat the procedure,” said Charlie.

 “Ok, Charlie, let’s give it a go,” said Jake.

How long would you say this game continued on average until Jake won or lost, and what could be any amount Jake paid to charity after playing ‘Four Card Deal’ ten times?