Ken's blog

Barnaby of the Barnaby and Bartholomew East India Trading Co. was worried as none of his ships had returned so far this month of May, 1776.

Lately, statistics were not very promising. Only six out of ten ships were returning, whether due to bad weather or piracy or both.

Five ships were due to return this month, but Barnaby could manage to survive somehow if three ships entered port.

What would you say was the probability that exactly three of Barnaby’s ships returned?

And the probability that at least three of Barnaby’s ships returned?

One Saturday afternoon, as Jack, now a full-fledged member, entered the Snake Eyes Dice Club in River City, he saw four persons throwing dice at a felt-covered table with Vince, the dealer.

“What’s up today, Vince?” asked Jack.

“Let me introduce you to Simon, Mary, Seamus and Henry here,” said Vince.

Polite hellos and smiles were exchanged.

“We’re playing a new game called “First Ace,” explained Vince.

“And how does it work, Vince?”

“Well, each person gets to throw a die in turn and the first one to get an ace wins the pot,” explained Vince. “If nobody throws an ace, I get the pot.”

“What does it cost to play the game?”

“Each player adds ten dollars to the pot per round, and I add 36 dollars,” said Vince.

“Interesting… Is this an honest game, Vince?” asked Jack, giving a skeptical look.

“As honest as most gambling games,” replied Vince with a smug wink.

“Sure, Vince. I’ll be heading for the lounge.”

Jack walked off, leaving Simon, Mary, Seamus and Henry with worried looks.

After ten rounds of “First Ace” what would you say Vince’s average gain or loss might be?

What about the average respective gains or losses of Simon, Mary, Seamus and Henry after ten rounds?

Is there any big winner in this game? Or big loser?

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?