WS MoreOrLess: Golden Ticket
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What is the main topic discussed in this episode?
This is the short edition of More or Less, first broadcast on the BBC World Service.
Hello and welcome to More or Less on the BBC World Service. I'm Charlotte MacDonald. This week, does the age of players make a difference to World Cup football results? But first, we're delighted that More or Less is attracting audiences of all ages.
What question did nine-year-old Isabel ask about the Golden Ticket?
My name is Isabel and I'm nine years old and we've been reading Charlie and the Chocolate Factory at school.
For those who are not familiar with Roald Dahl's book, we asked a panel of experts to summarise the plot for you.
The main character's Charlie. Charlie loves chocolate.
Who makes chocolate in Charlie's town?
His name's Willy Wonka.
How is the plot of Charlie and the Chocolate Factory summarized for children?
He has a big factory to make chocolate. Willy Wonka decides to send out five golden tickets. You have to go get a chocolate bar to find a ticket. And if you get the golden ticket, you'll go to Willy Wonka's factory.
So chocolate-loving Charlie Bucket was desperate to see inside Willy Wonka's factory. Our loyal listener Isabel set us this challenge.
My question is, what is the probability of Charlie Booker winning a golden ticket?
We sent Rob Easterway, author of a number of maths books, including Maths for Mums and Dads, to explain to Isabel's class how you work out the chance of Charlie winning one of the golden tickets.
Because I got a golden ticket. I got a golden ticket. I got a golden chance to make my way.
Who knows what probability is? Yeah, the chances of things happening. So how likely do you think it is that Charlie is going to win a golden ticket?
Not very likely.
What the book doesn't say is how many chocolate bars there were altogether. that Willy Wonka had made into which he could have put the golden tickets. Does anyone know how long it took in the book to run the competition between when it started and when Charlie got the last golden ticket? What do you think?
Is it something like a month?
Yeah, it's about a month's worth of chocolate for this competition. And one of the world's biggest selling chocolate bars is called a Kit Kat. Let's say that Wonka bars are the same as Kit Kat.
Whoa, whoa, whoa, that's ridiculous. The Kit Kat is a perfectly decent chocolate bar, but it's no whipple-scrumptious fudge-mallow delight.
How did Rob Eastaway estimate the number of Wonka bars and contest duration?
So five billion Wonka bars per year. We think they sell about... 5 billion Kit Kats every year. So how many months are there in a year? 12! Excellent. So 5 billion divided by 12, it's about 400 million. So how many golden tickets are there altogether? And there's 400 million chocolate bars altogether. Five out of 400 million is the same as, gosh, that's quite difficult.
How many fives are in 100, Sophia? 20. If there are 25 in 100, how many are there in 400, Sophia?
80 80 fantastic so there's about a one in 80 million chance of getting a golden ticket charlie didn't just buy one chocolate bar he got four so his chance of getting a golden ticket was actually about one out of 20 million. Does anyone know just how unlikely one out of 20 million is? Here's one way of thinking of it. Just imagine you were forming a queue outside the school, maybe two of you for every metre. So that means you would go for 10,000 kilometres. Where's 10,000 kilometres from here? Here to France. It's going to be even further than from here to France. Can anyone name me a city in South Africa?
Johannesburg.
So imagine a line of children from outside the classroom here going all the way to Johannesburg and only one of those children gets a golden ticket. That would be pretty unlikely, wouldn't it? Are you surprised? So, Isabel, what do you think of that answer?
It's quite big.
Are you happy you've got the answer to that now?
Yes.
Using Rob's back-of-the-envelope calculations, he reckons that Charlie had a 1 in 20 million chance of winning the golden ticket. Of course, those are actually the chances that any random individual would win the ticket. In fact, you could argue that Charlie's chances are 100%. Otherwise, he wouldn't be the main character of the book. Thank you to Rob Easterway, and thank you to the children of Belper Primary School in Derbyshire in the UK.
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Chapters
5 chapters
1
What is the main topic discussed in this episode?
0:00–0:35
2
What question did nine-year-old Isabel ask about the Golden Ticket?
0:35–1:01
3
How is the plot of Charlie and the Chocolate Factory summarized for children?
1:01–2:50
4
How did Rob Eastaway estimate the number of Wonka bars and contest duration?
2:50–6:05
5
How do you calculate the probability of finding one of five Golden Tickets?
6:05–9:32