# There are 15 white and 5 black balls in the urn. 5 balls are selected at random.

September 14, 2021 | education

| **There are 15 white and 5 black balls in the urn. 5 balls are selected at random. Find the probability that there are exactly 3 white balls among them.**

The total number of different sets when choosing 5 balls out of 20:

C (20.5) = 20! / (5! (20 – 5)!) = 16 17 18 19 20 / (1 2 3 4 5) = 15504.

Number of sets when choosing 3 out of 15 white balls:

C (15.3) = 15! / (3! (15 – 3)!) = 13 14 15 / (1 2 3) = 455.

Number of sets when choosing 2 black balls out of 5:

C (5,2) = 5! / (2! 3!) = 4 5/2 = 10.

The probability that out of 5 chosen balls, three balls will be white:

P (3) = C (15.3) C (5.2) / C (20.5) = 455 10/15504 = 0.293.

Answer: The probability of picking 3 white balls is 0.293.

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