Math-probability

[joonkimdds]

There are 3 blue, 4 green, 5 red balls. What is the probability of drawing a blue, a green and a red ball without replacement?

I thought answer should be 1/22 becuz
3/12 x 4/11 x 5/10 = 1/22 but that's not it.
The solution says I should multiply it by 6 but i don't know why.

Here is a similar question

Superwoman has 3 blue balloons, 4 green balloons and 5 red balloons. How many possible 3 balloon bouquets can she make?

Again, i thought it should be 1/22 but no.
This is actually different from previous one.
The previous one multiplied by 6, but this time we divide by 6


Basically I wanna know
when I should multiply and when I need to divide.
and also, when I don't have to do any of those two and just leave the answer 1/22.

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[vvvv]

There are 3 blue, 4 green, 5 red balls. What is the probability of drawing a blue, a green and a red ball without replacement?

I thought answer should be 1/22 becuz
3/12 x 4/11 x 5/10 = 1/22 but that's not it.
The solution says I should multiply it by 6 but i don't know why.

Here is a similar question

Superwoman has 3 blue balloons, 4 green balloons and 5 red balloons. How many possible 3 balloon bouquets can she make?

Again, i thought it should be 1/22 but no.
This is actually different from previous one.
The previous one multiplied by 6, but this time we divide by 6


Basically I wanna know
when I should multiply and when I need to divide.
and also, when I don't have to do any of those two and just leave the answer 1/22.

the first problem. you should find the pr of 3 balls from 12. it's 3C12. then find the pr of 1blue = 1C3, 1 green = 1C4, 1 red= 1C5

then (1blue * 1 red * 1 green)/ pro of 3C12 = 3/11

 

[vvvv]

There are 3 blue, 4 green, 5 red balls. What is the probability of drawing a blue, a green and a red ball without replacement?

I thought answer should be 1/22 becuz
3/12 x 4/11 x 5/10 = 1/22 but that's not it.
The solution says I should multiply it by 6 but i don't know why.

Here is a similar question

Superwoman has 3 blue balloons, 4 green balloons and 5 red balloons. How many possible 3 balloon bouquets can she make?

Again, i thought it should be 1/22 but no.
This is actually different from previous one.
The previous one multiplied by 6, but this time we divide by 6


Basically I wanna know
when I should multiply and when I need to divide.
and also, when I don't have to do any of those two and just leave the answer 1/22.

for the second problem. I assume that the all the red ball are identical, all the green balls are identical and the same with blue. so the problem ask how many ways to pick 3 ball from 3 different colors. pr= 3C3+3-1 = 3C5 = 10.

but if the balls are different, then pr= 3P12.

In my opinion, I think all red balls are identical, same with green and blue.

Does anyone know when to assume this?

 

[Zerconia2921]

There are 3 blue, 4 green, 5 red balls. What is the probability of drawing a blue, a green and a red ball without replacement?

I thought answer should be 1/22 becuz
3/12 x 4/11 x 5/10 = 1/22 but that's not it.
The solution says I should multiply it by 6 but i don't know why.


Want/Possible

3blue/12 x 4green/12 x 5red/12 = 60/1720



Here is a similar question

Superwoman has 3 blue balloons, 4 green balloons and 5 red balloons. How many possible 3 balloon bouquets can she make?

Again, i thought it should be 1/22 but no.
This is actually different from previous one.
The previous one multiplied by 6, but this time we divide by 6



n = 3!
3x2x1 = 6

Basically I wanna know
when I should multiply and when I need to divide.
and also, when I don't have to do any of those two and just leave the answer 1/22.

...

 

[joonkimdds]

the first problem. you should find the pr of 3 balls from 12. it's 3C12. then find the pr of 1blue = 1C3, 1 green = 1C4, 1 red= 1C5

then (1blue * 1 red * 1 green)/ pro of 3C12 = 3/11

bravo

 

[DentalP87]

There are 3 blue, 4 green, 5 red balls. What is the probability of drawing a blue, a green and a red ball without replacement?

I thought answer should be 1/22 becuz
3/12 x 4/11 x 5/10 = 1/22 but that's not it.
The solution says I should multiply it by 6 but i don't know why.

Here is a similar question

Superwoman has 3 blue balloons, 4 green balloons and 5 red balloons. How many possible 3 balloon bouquets can she make?

Again, i thought it should be 1/22 but no.
This is actually different from previous one.
The previous one multiplied by 6, but this time we divide by 6


Basically I wanna know
when I should multiply and when I need to divide.
and also, when I don't have to do any of those two and just leave the answer 1/22.

hello. so ehre goes my explanations:

1) you are right on the 3/12 x 4/11 ... = 1/22 part
but you forgot to times this by the number of ways that these balls can be chosen, ie. you can choose one red-blue-green, blue-red-green... etc

so, you have to times 1/22 by 3P3 to account for the different ways of choosing the balls

2) This question has nothing to do with probability, so you shouldn't even have a fraction as an answer.

My answer would be 12C3, since order here would not matter (ie. blue-green-red is same as blue-red-green) --> but this question is very unclear imo

hope this helps