SOLUTION: A Random Sample of 4 Members of a members a 150 members club has shown that 3 prefer no smoking in the club house dining room. What is the probability that this will occur if in fa

Question 1169929: A Random Sample of 4 Members of a members a 150 members club has shown that 3 prefer no smoking in the club house dining room. What is the probability that this will occur if in fact only 20% of members prefer no smoking in the dining room. Answer=0.0240
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
4 ways for this to occur.
(30/150)(29/149)(28/148)(120/147)--the other three ways have the same numbers but ordered differently.
so 4* the above is 0.0240
or 30C3*120C1/150C4, which gives the same results
notice how the parts before the C add to 150 on top and after add to 4 on the bottom. That's what you try to set up in a hypergeometric distribution.

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