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02nd Mar 2024

The Chase’s baffling maths question leaves Chaser and contestant stumped

Ryan Price

Do you think you can answer it?

We’ve all experienced that moment when watching The Chase when you get on a roll of getting the first two or three questions right and then a really tough one comes around and you can’t even remember your own name.

Well, something similar happened on Wednesday night’s episode of the ITV game show.

RAF pilot Andrew from Anglesey stepped up under the bright studio lights to take on the chaser.

The Sinnerman, real name Paul Sinha, had earlier in the episode dismantled contestants Barry from Rugby and Danny from Plymouth in their Head to Head rounds.

(Photo courtesy of ITV/Screengrab)

Andrew started with confidence after showing great general knowledge in his Cash Builder round, and seemed to be getting into a bit of rhythm until a question seemed to throw both the 32 year old pilot and the 53 year old brainiac.

The question, known by maths experts online as the Birthday Paradox was: “How many people need to be in a room to give a 99.9% chance that two of them share the same birthday?” 

The multiple-choice options were 25, 50, or 75.

Both Andrew and The Sinnerman answered 25.

Andrew told host Bradley Walsh: “I think it’s one of those weird maths [questions], it doesn’t sound very distinctive – but it’s an unusual number so I went for the low”.

Walsh seemed unsure and said: “Got to be much higher than that?”

When the answer was revealed to be 75, both the contestant and chaser were stumped, while Walsh couldn’t get over the fact that the Sinnerman had got the question wrong.

The Sinnerman said: “NOO!” “I knew it was low so went for the lowest, I’d heard the fact before but clearly not well enough!”

To be fair to both, all of us here at Joe HQ had to google The Birthday Paradox and educate ourselves on the mathematical theory aswell.

Here’s the full explanation behind the dumbfounding question.

The birthday paradox, also known as the birthday problem, states that in a random group of 23 people, there is about a 50 percent chance that two people have the same birthday. Is this really true?

There are multiple reasons why this seems like a paradox. One is that when in a room with 22 other people, if a person compares his or her birthday with the birthdays of the other people it would make for only 22 comparisons—only 22 chances for people to share the same birthday.

But when all 23 birthdays are compared against each other, it makes for much more than 22 comparisons. How much more? Well, the first person has 22 comparisons to make, but the second person was already compared to the first person, so there are only 21 comparisons to make. The third person then has 20 comparisons, the fourth person has 19 and so on. If you add up all possible comparisons (22 + 21 + 20 + 19 + … +1) the sum is 253 comparisons, or combinations. Consequently, each group of 23 people involves 253 comparisons, or 253 chances for matching birthdays.

In a room of just 23 people there’s a 50-50 chance of at least two people having the same birthday. In a room of 75 there’s a 99.9% chance of at least two people matching.

Luckily for Andrew, the fact that the Sinnerman got the question wrong too meant that he could progress to the next question, but that then happened to be a question about musical theatre, a subject he admitted he knew nothing about.

Luckily, he correctly guessed that the song, Lose Ur Head, is from the musical Six and went through to the Final Chase.

In the last round, Andrew was paired up with another contestant called Wendy and between them they answered 13 questions correctly.

The Chaser then needed 15 correct answers to beat them which of course he managed to do with a whopping 44 seconds to spare.

While it was a defeat in the end for Andrew, he can take solace in the fact that he will go down in The Chase folklore as the contestant who was equally as clueless about the birthday paradox as the Sinnerman.

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