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Rom4ik [11]
2 years ago
6

Conce

Mathematics
1 answer:
weeeeeb [17]2 years ago
3 0

Answer:

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:

P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}

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:

C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

In this question, we have that:

20 patients means that N = 20

Sample of 8 means that n = 8

9 have the heart problem, so k = 9

What is the probability that exactly 6 patients will die?

This is P(X = 6).

P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}

P(X = 6) = h(6,20,8,9) = \frac{C_{9,6}*C_{11,2}}{C_{20,8}} = 0.0367

0.0367 = 3.67% probability that exactly 6 patients will die

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