find the probability

Question

35 Blue (B); 20 Large (L), 15 Small (S)

30 Yellow (Y); 5L, 25S

20 Green (G); 15L, 5S

15 Red (R); 10L, 5S

 calculate

1. p(R½L)

 

2. p(all R in a sample of 3 selected with replacement)

 

3. p(the frequency of Y in a sample of 4 selected with replacement = .25)

 

4. p(at least 1 G in a sample of 3 selected without replacement)

 

5. p(no more than 1 S in a sample of 4 selected without replacement)

Answer 1

There are a lot of questions here.  I'll show you how to do number 2 (because I don't know what R½L means in number 1).  If you need help with the others try posting them individually as they all involve a non-trivial explanation.  

 

There are 35 + 30 + 20 + 15 = 100 total possibilities.  Of these 15 are R.  So P(R) in a single sample is 15/100 = 0.15.  If you sample with replacement that means you put the R you took back before you take the next sample, so P(R) is also 0.15 on the second sample.  With replacement you again return the R and so P(R) = 0.15 on the third sample as well.  So the probability that all 3 selections are R is 0.15*0.15*0.15 = 0.003375