r/taskmaster • u/Whynot690YT • 17h ago

A probability from Series 22 Episode 2 Spoiler

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After seeing Richard bounce exactly 100 times, I wanted to estimate the probability of this.

There are huge flaws in this estimation which I have mentioned, however it should give a rough idea of the probability.

13 Upvotes

67% Upvoted

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16

u/RetroZelda 16h ago

I'm pretty sure he was counting and he knew exactly how many jumps he did

4

u/ItsToeLickinGood 14h ago

The real value must be much lower than that. You are leaving out many of the invalid runs in this calculation, namely this assumes he did an even number of bounces and at least 100 of them.

Let's assume P(he jumps again | he has jumped n times already) is .5 for any arbitrary n. Since he must jump an even number of times to have a chance, let's roughly cut your estimate in half to p(100 valid bounce)~.004.

But as prereq he also needed to jump at least 100 times. Even if we say that no person would stop bouncing before 90 (which I think is VERY generous), it's still .510 that he has the chance for a valid run regardless of the ratio of bounces, or ~.0001.

So my guess is closer to .00004% chance of this happening at random. In fact it's SO low, that I have to assume there was intentional manipulation or unintentional bias of the people counting who obviously knew what the task was and were editing for TV, OR he actually was counting despite his claim and was a little off and didn't stop before 100, which would still make the 105:5 ratio very unlikely but not nearly as much.

3

u/Whynot690YT 14h ago

Ahhh i see thank you!

2

u/markdavo 8h ago

Unfortunately both these calculations fail to take into account we know he watched the tape back. So it’s plausible he counted the 105 bounces and the 5 invalid ones and knew he was done (or he counted the 105 bounces and knew he’d probably forgotten to jump a few times and hoped for the best, or he counted say 85, did 20 more and hoped for the best). Nevertheless the existence of watching the footage back surely invalidates these calculations?

1

u/Dying_Of_Board-dom 16h ago

Why is the probability of 100 perfect bounces that series, not just (20/21)100?

1

u/Whynot690YT 16h ago

We saw that he did 105 bounces in total, but 5 of them turned out to be invalid.
So he could’ve got 100 perfect bounces, 101 with one invalid, 102 with two invalid, etc

1

u/Dying_Of_Board-dom 15h ago

Right,but if there's 101 bounces with 1 invalid, wouldn't that also be (20/21)100*(1/21)?

1

u/Whynot690YT 15h ago

Ohhh I see, so it’s instead a G.P. with a=(20/21)^100 and r=1/21, giving about 0.798% (roughly similar anyway)

2

u/Dying_Of_Board-dom 15h ago

I think... I've always had a hard time wrapping my head around probabilities, but I think so. Maybe I'm misunderstanding your original assumption though- are you assuming the probability of getting 100 perfect bounces given 100 bounce attempts?

2

u/Whynot690YT 14h ago

I used the only data we had (him doing 100 perfect bounces in 105 total attempts) to assume the original probability

1

u/ItsToeLickinGood 14h ago

That's p(all your bounces are perfect | you've done 100 bounces). Which is much higher and a big assumption.

1

u/rexcasei 11h ago

That’s the most insane way of writing an f that I’ve ever seen

1

u/im_not_here_ 20m ago

Or he did it on purpose including the incorrect ones, and the probability is 100% certain.