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?