What kind of distribution should I use to this question?

Question

From every 200 students in High School, 20 students failed. If we were to pick 40 students from the class. Calculate:

(a) the probability of getting 8 failed students. (b) the expected value for the failed students out of 40 students.

Should I use binomial distribution or hypergeometric?

Answer 1

The sampling procedure is not told thus you can assume if you draw with or without replacement first and then solve the exercise accordingly.

• Binomial

$$\mathbb{P}[X=8]=\binom{40}{8}\left(\frac{1}{10}\right)^8\left(\frac{9}{10}\right)^{32}\approx 0.026$$

• Hypergeometric

$$\mathbb{P}[X=8]=\frac{\binom{20}{8}\binom{180}{32}}{\binom{200}{40}}\approx 0.018$$

The expectation is the same in the two cases...