Survey Statistic Problem

Question

I have no idea how to solve this. Someone please explain to me.

 

427 different women were randomly selected and asked what they buy online, and 162 of the women says clothes. 

 

If 10 different women are randomly selected without replacement, what is the probability that none of them chose clothes?

 (The answer hints 5% guideline to cumbersome calculation but I'm just really confused)

Answer 1

Ellis,

        This is the same as the classical urn containing w white balls and b black balls. We now sample n without replacement the number X of white balls in the sample follows a Hypergeometric distribution 

 

P(X=k)=(_WC_k*_bC_(n-k))/_(w+b)C_n)

 

We can now identify these urn variables w,b,n and k with the variables in your problem

 

w+b=427 women sampled

b=162 women that bought clothes on line

w= 265 women that did not buy clothes on line

n=10 the number randomly selected with out replacement

 

and we want k=0 i.e. the probability that none of 10 bought clothes on line.

 

I got P(X=0)=.0000517 very unlikely!!

 

Hope this helps

Jim

 

 

Answer 2

Hi Ellis,

There 427 different women, 162 of them buy clothes online and 265 of them do not buy clothes online

10 women  are chosen at random without replacement

Ler E denote the event that none of the women buy clothes online

Notice that there is no replacement

 

First randomly selected has probability     = 265/427

Second randomly selected has probability = 264/426 

Third randomly selected has probability     = 263/425 

Do you see the trend

 

P(E) = (265/427)(264/426)(263/425)(262/424)(261/423)(260/422)(259/421)(258/420)(257/419)(256/418)

       =0.00794

A simpler way is to number of ways of choosing 10 women from the 265 who did not buy clothes online

divide by number of ways of choosing 10 women who do not buy clothes online out of 427.

P(E) = ²⁶⁵C₁₀/⁴²⁷ C₁₀

       =(265!/10!255!)/(427!/10!417!)

       =(265!/255!)(417!/427!)

 

Answer 3

If 162 out of 427 said yes the probability of a "success" is 162/427 = p.

 

Consider this a binomial experiment with n=10 and and zero successes.

 

 

Need more help comment back.