/sci/ - Science & Math » Thread #13858518

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Stuck on probability

Anonymous Tue 16 Nov 12:11:02 2021 No.13858518 View Reply Original Report

Quoted By: >>13858627 >>13858668

Let's say there are 898 types of pokemon cards, each of them is a pokemon, 59 of which are legendary. Each card has a flat chance of being included in a booster pack.

A booster pack contains 10 random cards, what is the probability of getting a booster pack that contains exactly 1 legendary?

Anonymous

Anonymous Tue 16 Nov 2021 12:12:44 No.13858521 Report

Quoted By: >>13858565

(9 choose 898-59)/(10 choose 898+59)

Anonymous

Anonymous Tue 16 Nov 2021 12:33:38 No.13858565 Report

Quoted By: >>13858651

>>13858521
>9 choose 898-59
I don't get it, if that's C(9, (898-59)), how does that work? n must be greater than r

Anonymous

Anonymous Tue 16 Nov 2021 12:56:25 No.13858627 Report

Quoted By: >>13858721

>>13858518
10*59*839^9/898^10 ~ 35.6%

Anonymous

Anonymous Tue 16 Nov 2021 13:17:33 No.13858651 Report

Quoted By: >>13858721

>>13858565
Yeah there's a mistake. You choose the legendary card: 59 choices. You select 9 other nonlegendary cards (9 choose 898-59). You divide with all possible 10 card combinations (10 choose 898+59)
59* (9 choose 898-59)/ (9 choose 898+59).

Anonymous

Anonymous Tue 16 Nov 2021 13:27:49 No.13858668 Report

Quoted By: >>13858721

>>13858518
Isn't this just looking for the chance of a card being legendary (6.6%) multiplied by the probabilities of 9 cards being normal (93.9^9%)? So about 3.56%

Anonymous

Anonymous Tue 16 Nov 2021 13:58:17 No.13858721 Report

Quoted By:

>>13858627
>>13858651
>>13858668
seems like a tough pickle considering everybody gets different results.
Aren't there 4,5131×1022 possible combinations that do not include a legendary considering (898?59)!÷(10!×((898?59)?10)!)
and there 8,936348468×1022 combinations in total which would mean there is at least 50.5% chance of getting at least one legendary.
So, I don't odds of getting exactly one, but I'd imagine it'd be the most likely way to get a legendary, thus 3.56% seems particularly unlikely

Anonymous

Anonymous Tue 16 Nov 2021 20:03:43 No.13859603 Report

Quoted By:

Just weigh them for rarer cards wight more. Or xray. Or perfurate minimally and let doggo sniff the rarer cards.

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