Answer:
0.0164 probability that exactly 11 black balls are drawn
Step-by-step explanation:
The balls are drawn 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:
Total of 88 + 88 = 176 balls, so
33 balls are drawn, so
We want 11 black balls(sucesses), so
There are 88 black balls, so
Then
0.0164 probability that exactly 11 black balls are drawn