Answer:
0.1667 = 16.67% probability that they are both black.
Step-by-step explanation:
The balls are drawn without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
In which:
x is the number of successes.
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:
5 + 4 = 9 balls, which means that
4 are black, which means that
2 are chosen, which means that
What is the probability that they are both black?
This is P(X = 2). So
0.1667 = 16.67% probability that they are both black.