Answer:
0.294 = 29.4% probability that none of the chosen entrees contain spinach.
Step-by-step explanation:
The choices of entrees are chosen without replacement, which means that the hypergeomtric distribution is used 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.
13 different entrees for an important banquet
This means that
3 of which contain spinach.
This means that
The guests will have a choice of 4 entrees.
This means that
What is the probability that none of the chosen entrees contain spinach?
This is P(X = 0). So
0.294 = 29.4% probability that none of the chosen entrees contain spinach.