Question

An investment manager have nine projects at hand - three are domestic projects and six are overseas projects. He needs to choose two of them to invest. All projects have equally expected returns. Hence two projects will be randomly selected from the nine projects. Let

Answer 1

Let X be the number of domestic projects selected. Then X is not a Binomial random variable.

What is a success? What is a failure?

$$P(0 \ domestic)={6 \over 9}\cdot{6-1 \over 9-1}={5 \over12}$$

$$P(1 \ domestic)={\binom{3}{1}\binom{6}{1} \over \binom{9}{2}}={3\cdot6 \over{9! \over 2!(9-2)!}}={1 \over 2}$$

$$P(2 \ domestic)={3 \over 9}\cdot{3-1 \over 9-1}={1 \over12}$$

Answer: X is not a Binomial random variable.