# Question

(a) An urn contains n white and m black balls. The balls are withdrawn one at a time until only those of the same color are left. Show that, with probability n/(n + m), they are all white.

Imagine that the experiment continues until all the balls are removed, and consider the last ball withdrawn.

(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?

Write P{R} = P{RBG} + P{RGB}, and compute the probabilities on the right by first conditioning on the last species to be removed.

Imagine that the experiment continues until all the balls are removed, and consider the last ball withdrawn.

(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?

Write P{R} = P{RBG} + P{RGB}, and compute the probabilities on the right by first conditioning on the last species to be removed.

## Answer to relevant Questions

Let A,B, and C be events relating to the experiment of rolling a pair of dice. (a) If P(A|C) > P(B|C) and P(A|Cc) > P(B|Cc) either prove that P(A) > P(B) or give a counterexample by defining events A,B, and C for which that ...The National Basketball Association (NBA) draft lottery involves the 11 teams that had the worst won–lost records during the year. A total of 66 balls are placed in an urn. Each of these balls is inscribed with the name of ...A and B play the following game: A writes down either number 1 or number 2, and B must guess which one. If the number that A has written down is i and B has guessed correctly, B receives i units from A. If B makes a wrong ...Find Var(X) and Var(Y) for X and Y as given in Problem 21. Problem 21 Four buses carrying 148 students from the same school arrive at a football stadium. The buses carry, respectively, 40, 33, 25, and 50 students. One of the ...Suppose that a biased coin that lands on heads with probability p is flipped 10 times. Given that a total of 6 heads results, find the conditional probability that the first 3 outcomes are (a) h, t, t (meaning that the first ...Post your question

0