Probability Without Replacement - urgent! ?

[amr12880rt]

Hey there, any help be greatly appreciated!

Probability without replacement. There are 38 different colored balls in the drawing. 35 are 35 different colored balls, and three are red. We are going to pull 16 balls in individual pulls. Once a ball is pulled it is tossed. What are the chances that during those 16 pulls that I never pull a red one?

 

[Deleted member 4993]

Hey there, any help be greatly appreciated!

Probability without replacement. There are 38 different colored balls in the drawing. 35 are 35 different colored balls, and three are red. We are going to pull 16 balls in individual pulls. Once a ball is pulled it is tossed. What are the chances that during those 16 pulls that I never pull a red one?

Please share your work/thoughts about this problem.

 

[Dr.Peterson]

Hey there, any help be greatly appreciated!

Probability without replacement. There are 38 different colored balls in the drawing. 35 are 35 different colored balls, and three are red. We are going to pull 16 balls in individual pulls. Once a ball is pulled it is tossed. What are the chances that during those 16 pulls that I never pull a red one?

In order to help effectively, we need to know what help you need, which requires you at least to show some work or ask specific questions.

By way of help, I'll ask you a question: Can you calculate the denominator of the probability using combinations or permutations? Then, what would the numerator look like?

If you prefer another approach, show us what it is.

 

[Steven G]

I would think hypergeometric.

 

[amr12880rt]

So actually, I substituted this scenario to make it easy but here’s the real life deal. Signed my three 4-year-olds up for a local pre-k program. 38 kids on the potential list. They draw 16 names. Out of those 16, none of them were any of my three daughters. What are the chances that none of my three daughters’ names were pulled during those 16 chances?

 

[Dr.Peterson]

So actually, I substituted this scenario to make it easy but here’s the real life deal. Signed my three 4-year-olds up for a local pre-k program. 38 kids on the potential list. They draw 16 names. Out of those 16, none of them were any of my three daughters. What are the chances that none of my three daughters’ names were pulled during those 16 chances?

Okay, so this is not for a class, just about a class! I suppose we can give the answer, then:

There are C(38,16) = 2.22*10^10 ways to choose 16 names; there are C(35,16) = 4.06*10^9 ways to choose 16 excluding yours. So the probability that this would happen at random is 18.25%.

That's a little less than 1/5 So, if this drawing were repeated 5 times, that would likely happen once. That's too high a probability for a statistician to say it isn't just chance.

One might wonder if they somehow treated yours as a group to avoid splitting them up. For comparison, if they had 13 sets of triplets and chose 5 of them (so they choose 15 of 39 kids, but keeping sets together), the probability of excluding yours would be C(12,5)/C(13,5) = 61.5%, so you'd be more likely to lose out. And in the actual drawing, the probability that all three of yours would be chosen would be C(35,13)/C(38,16) = 6.6%.