#Help

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sudden spoke
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A box containing 11 balls, numbered from 1 to 11, is drawn at random and placed on the table. What is the probability that the sum 6 of balls drawn is odd? answer should be 118/231

upper knotBOT
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void maple
sudden spoke
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they all same

void maple
sudden spoke
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6

void maple
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Oh, ok. Not sure why you omitted that.

sudden spoke
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mistake

void maple
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We want an odd sum, so the number of odd-numbered balls must be odd. The number of even-numbered balls is irrelevant.

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So, consider the case when we have 1 odd ball, then 3, then 5.

sudden spoke
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yeah i thought about this

sudden spoke
void maple
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Alright, and what did you get?

sudden spoke
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i tried but something wrong was

void maple
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Well, I checked this approach just in case, and it does give the correct answer. So, try arriving to it.

sudden spoke
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wait a second

sudden spoke
sudden spoke
void maple
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Almost what?

sudden spoke
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can you show me how you did calculations?

void maple
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Well, I just used hypergeometric distribution. However, I'd like to see what you did first.

sudden spoke
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hard to explain

sudden spoke
sudden spoke
void maple
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Oh, you're doing it like that.

void maple
sudden spoke
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then

void maple
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Although, I think it would be easier to look at unordered collections of balls.

sudden spoke
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5x4x3x2x1x6+6x5x4x3x2x5=720+3600 6x5x4x5x4x3x2=1440 14400+4320=18720

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18720/332640=117/2079

sudden spoke
void maple
sudden spoke
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can you show me?

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bcs i first time hear that

sudden spoke
rain linden
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@void maple

number of odd balls - 6
even balls - 5

6 x 5 x 4 x 3 x2 x 1 + 6x5 x 5 x4 x 3 x 2 + 6 x 5 x 4 x 5 x 4 / (11 x 10 x 9 x 8 x 7 x6 )

Is the numerator not including every situation for each case or something? im getting 8/231 indicating that something is wrong with the amount of cases being calculated?

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this is why I hate probability 😢

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hold on

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every case is being repeated lol

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im permuting not using groups

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so the total cases are 11C6

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462

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hm now for the individual ones

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6C1 * 5C5 = 6

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6C3 * 5C3 = 200

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6C5 * 5C1 = 30

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ok

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there we go

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lol

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I was counting like 1 3 4 6 8 2 and 3 1 4 6 8 2 as different cases with permutations 💀

rain linden
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u dont needa look into the name too much its not that deep its just one strcuture of calculating probability for a specific case

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like for example

if we had Ball A, Ball B, Ball C, and Ball D

and we wanted to see how many ways we can grab 2 of the balls and 2 of them are either A, B, or C using ur original method we'd get

3 balls

3 * 2, but thats not that case

because lets list out all of the cases

its basically saying

Ball A - [ Ball B or C

Ball B - [ Ball A or C

Ball C - [ Ball A or B

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which gives us 6 choices

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but wait theres repeating cases

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Ball A and Ball B is the same thing is Ball B and Ball A

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so we need to use combinations not permutations

void maple
rain linden
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Yeah I think the wording just confused him

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He prob knows what it is

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I got confused too when I saw hypergeometric distribution until I searched it up lol