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(a) An urn contains n white and m black balls. Hie balls
Chapter 3, Problem 7TE(choose chapter or problem)
Problem 7TE
(a) An urn contains n white and m black balls. Hie balls are withdrawn one at a time until only those of the same color are left. Show that with probability n/(n + m), they arc all white.
(b) A pond contains 3 distinct species of fish, which we will call the Red, Blue, and Green fish. There are r Red, b Blue, and g Green fish. Suppose that the fish are removed from the pond in a random order. (That is, each selection is equally likely to be any of the remaining fish.) What is the probability that the Red fish are the first species to become extinct in the pond?
Questions & Answers
QUESTION:
Problem 7TE
(a) An urn contains n white and m black balls. Hie balls are withdrawn one at a time until only those of the same color are left. Show that with probability n/(n + m), they arc all white.
(b) A pond contains 3 distinct species of fish, which we will call the Red, Blue, and Green fish. There are r Red, b Blue, and g Green fish. Suppose that the fish are removed from the pond in a random order. (That is, each selection is equally likely to be any of the remaining fish.) What is the probability that the Red fish are the first species to become extinct in the pond?
ANSWER:
Step 1 of 2
(a)
It is given that there are n white balls and m black balls in an urn.
Balls are drawn one at a time until same color balls are left.Using this we need to show that
is the probability that all the balls left are white.
There are n white balls and m black balls. So the total number of balls is n+m.
If n balls are removed from the urn, then the probability becomes
.
Hence the proof.