A chef is choosing from 13 different entrees for an important banquet, 3 of which contain spinach. The guests will have a choice of 4 entrees. The chef has decided to choose the 4 at random. Write your answers as a decimals rounded to the nearest thousandth. What is the probability that none of the chosen entrees contain spinach

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.

1. minimum

2. 6400

3. eight

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