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AnnZ [28]
2 years ago
9

A bag contains five white balls and four black balls. Your goal is to draw two black balls. You draw two balls at random. What i

s the probability that they are both black
Mathematics
1 answer:
NARA [144]2 years ago
8 0

Answer:

0.1667 = 16.67% probability that they are both black.

Step-by-step explanation:

The balls are drawn without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes 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 successes.

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:

5 + 4 = 9 balls, which means that N = 9

4 are black, which means that k = 4

2 are chosen, which means that n = 2

What is the probability that they are both black?

This is P(X = 2). So

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

P(X = 2) = h(2,9,2,4) = \frac{C_{4,2}*C_{5,0}}{C_{9,2}} = 0.1667

0.1667 = 16.67% probability that they are both black.

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