Well,

first of all, welcome to this forum from (maybe the only) french guy in the zone !! ;-)

preliminary : the exact model

let 's suppose there are N = 1,000 participants : 500 males, 500 females.

then, the favrorable cases are :

MMF - MFM - FMM

the probability of each case is :

P(MMF) = (500/1000) * (499/999) * (500/998)

and the answer is :

P(investigator will draw at least two males) = C(3,2) * P(MMF)

now, here, in the binomial model, we will suppose that, as we are in a large on-the-job training program,

N is "great" meaning : the proba is constant (approximation)

therefore :

(499/999) # 1/2

(500/998) # 1/2

therefore the proba of "success" (drawing a male) is constant :

p = 1/2 ==> proba of flaw : q = 1 - p = 1/2

therefore we get a classical binomial distribution:

P(investigator will draw at least two males) = C(3,2) * p^2 (1-p)^(3-1)

P(investigator will draw at least two males) = 3/8

= 37.5%

hope it' ll help !!

PS: if you want good answers, do not forget to give Best Answers..... to me, or anybody else, or course provided the answer deserves one !

this is to encourage people to answer !! ;-)

In this particular situation, it does not matter if the 3 participants are selected with or without replacement, nor does it matter how many participants are of each gender in the study (as long as there are 2 or more participants of each gender, and there are the same number of participants of each gender). We can use symmetry to solve this problem.

Because half of the participants are male and half are female, clearly

P(at least 2 of 3 are males) = P(at least 2 of 3 are females).

Furthermore, the events "at least 2 of 3 are males" and "at least 2 of 3 are females" are complementary (exactly one of these two events must occur), so

1 - P(at least 2 of 3 are males) = P(at least 2 of 3 are females).

From these two facts, 1 - P(at least 2 of 3 are males) = P(at least 2 of 3 are males).

Therefore, 2*P(at least 2 of 3 are males) = 1; P(at least 2 of 3 are males) = 1/2.

It follows that the probability that at least 2 of the 3 selected participants are males is 1/2.

Have a blessed, wonderful 4th of July!