# The urn contains 10 blue and 6 green balls. 4 balls are chosen at random. What is the likelihood that they are all green?

March 29, 2021 | education

| There are 10 + 6 = 16 balls in the urn.

The probability of choosing the first green ball out of 16: p1 = 6/16.

The conditional probability of choosing the second green ball out of the remaining 15, provided that the green one is chosen first: p2 = 5/15.

The conditional probability of choosing the third green ball out of the remaining 14, provided that the first and second ones are green: p3 = 4/14.

The probability of choosing the fourth green ball is p4 = 3/13.

By the probability multiplication theorem, the probability of choosing all 4 green balls is:

P (4) = 6/16 5/15 4/14 3/13 = 0.00824.

Answer: The probability that all the selected balls are green is 0.00824.

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