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An urn initially contains 5 white and 7 black balls. Each
Chapter 3, Problem 14P(choose chapter or problem)
Problem 14P
An urn initially contains 5 white and 7 black balls. Each time a ball is selected, its color is noted and it is replaced in the urn along with 2 other balls of the same color. Compute the probability that
(a) the first 2 balls selected are black and the next 2 are white;
(b) of the first 4 balls selected, exactly 2 are black.
Questions & Answers
QUESTION:
Problem 14P
An urn initially contains 5 white and 7 black balls. Each time a ball is selected, its color is noted and it is replaced in the urn along with 2 other balls of the same color. Compute the probability that
(a) the first 2 balls selected are black and the next 2 are white;
(b) of the first 4 balls selected, exactly 2 are black.
ANSWER:
Step 1 of 2
An urn contains 5 white and 7 black balls. Each time a ball is selected, its color is noted and it is replaced in the urn along with 2 other balls of the same color.
a.) The claim is to find the probability that the first 2 balls selected are black and the next 2 bare white.
Let W = white ball and B = black ball
We have 5 white and 7 black balls.
For first black, p =
The second black , p =
The third white , p =
fourth white , p =
Then, P(,
,
,
) = (
) (
) (
) (
)
=
Therefore, the probability that the first 2 balls selected are black and the next 2 bare white is .