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here are 55 black balls and 99 red balls in an urn. If 44 balls are drawn without replacement, what is the probability that exactly 33 black balls are drawn? Express your answer as a fraction or a decimal number rounded to four decimal places.

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vlatkostojanovic

Answer:

P=0.0899.

Step-by-step explanation:

We know that are 5 black balls and 9 red balls in an urn. If 4 balls are drawn without replacement. We calculate the probability that exactly 3 black balls are drawn.

Therefore, we have 14 balls in an urn.

We calculate the number of possible combinations:

[tex]C_4^{14}=\frac{14!}{4!(14-4)!}=1001\\[/tex]

We calculate the number of favorable combinations:

[tex]C_3^5\cdot C^9_1=10\cdot 9=90[/tex]

Therefore, the probability is:

P=90/1001

P=0.0899.

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