There are 25 pens in a container on your desk. Among them, 20 will write well but 5 have defective ink cartridges. You will select 2 pens (without replacement) to take to a business appointment. Calculate the probability that both pens are defective.

3.33% probability that both pens are defective.

Step-by-step explanation:

The pens are chosen without replacement, so we use the hypergeometric distribution to solve this question.

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

is the number of different combinations of x objects from a set of n elements, given by the following formula.

In this question:

2 defective, so x = 2.

25 pens, so N = 25.

Two pens will be selected, so n = 2.

5 are defective, so k = 5.

3.33% probability that both pens are defective.

answer: -0.5 would be the most likley outcome

step-by-step explanation:

cross multiplying, we get :

⇒ (3) × (5) = (9) × (x)

⇒ 15 = 9x