Answer to Question #220804 in Statistics and Probability for ansha

Question

 

A Statistics department purchased 24 hand calculators from a dealer to have a supply on hand for tests for use by students who forget to bring their own. Although the department was not aware of this, three of the calculators were defective and gave incorrect answers to calculations. Students who have forgotten their own calculators are allowed to select one of the Department's (at random). Suppose that five students forgot to bring their calculators.

(Note: Use hypergeometric probability distribution to calculate probabilities)

 

a)    What is the probability that exactly two of these students select a defective calculator?

 

 

Answer 1

N=24

n=5

x=2

k=3

Hypergeometric distribution

$P(X) = \frac{\binom{k}{x} \binom{N-k}{n-x}}{\binom{N}{n}} \\ P(2) = \frac{\binom{3}{2} \binom{24-3}{5-2}}{\binom{24}{5}} \\ P(2) = \frac{3 \times 1330}{42504} \\ P(2) = 0.0938$