Probability problem

[zolvtas]

Hi!
It would be awesome if someone gave me guidance about the following problem:

Problem
A group of people are asked how to deal with energy shortage. Here are the results:

Response	Number
More production	336
More conservation	490
Both	91
No opinion	32
Total	949

Suppose we select three people at random from this sample. Answer the following:
a) What is the probability that all three responded "develop wind and solar"?
b) What is the probability that none responded "equally important"?
c) What assumption did you make in computing these probabilities?

Correct answer
a) 0,205
b) 0,805
c) Responses are independent.

My question
a) The only solution that I can come up with is --> 581/949*580/948*579/947=0,229. This is answer is close but here I have added the row "both" and "more conservation", when my opinion is that row "both" at the most should only be added with one half, that is 45,5.

b) The only solution that I can come up with is --> 917/949*916/948*915/947=0,902

Please comment on a) and b) as well as the rules (if any) that are applied on this problem.


Thanks!

 

[AmandasMathHelp]

It doesn't make sense to add only half of the "both" responders. Either the question wants only the production category or it wants the production and the both category. Since the actual answer is lower, my guess is for part 'a' just use the "production" responses. It's a little weird that the question asks specifically for "develop wind and solar" when the chart does not include that wording so if that doesn't work please post a picture of the entire problem so we can understand better.

For part b it looks like you subtracted the number of people that had no opinion but the wording "equally important" sounds like it is referencing the the "both" category. They want the probably than none responded "both". Try that.

Side note: when you post on here you might want to explain that you are using "," and "." differently than in other countries. It took me a while to understand your post and remember that in some countries decimals are written using commas instead of periods.

 

[zolvtas]

Thanks for input!

From Sweden, didnt think about that. Will do next time!