## Conce Unknown to a medical researcher, 9 out of 20 patients have a heart problem that will result in death if they receive the test dr

Question

Conce
Unknown to a medical researcher, 9 out of 20 patients have a heart problem that will result in death if they receive the test drug. 8 patients are randomly selected to
receive the drug and the rest receive a placebo. What is the probability that exactly 6 patients will die? Express your answer as a fraction or a decimal number rounded to
four decimal places.

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3 years 2021-09-03T10:50:09+00:00 1 Answers 13 views 0

0.0367 = 3.67% probability that exactly 6 patients will die

Step-by-step explanation:

The patients are chosen without replacement, which means that the hypergeometric 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.

In this question, we have that:

20 patients means that

Sample of 8 means that

9 have the heart problem, so

What is the probability that exactly 6 patients will die?

This is P(X = 6).

0.0367 = 3.67% probability that exactly 6 patients will die