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A First Course in Probability (10th Edition)

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

You have three pens coloured blue, red, and green. You pick one at random and then you pick another without replacement. (a) Find the conditional probability that the second pen is blue, given the first pen is red.
(b) Find the conditional probability that the first pen is red, given the second pen is blue.

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A gambler has a fair coin and a two-headed coin in his pocket. He randomly selects one of the coins. (a) Suppose that he flips the selected coin twice, and both show heads. Find the probability that the selected coin is the fair coin. (b) Suppose that he flips the selected coin four times, and all show heads. Find the probability that the selected coin is the fair coin.
Sally and Mike are playing frisbee at the beach. When Sally throws the frisbee the probability is 0.13 that it comes back to Sally, the probability is 0.7 that it goes to Mike, and the probability is 0.17 that the dog runs away with the frisbee. When Mike throws the frisbee there is a 0.62 probability that Sally gets it, a 0.27 probability that it comes back to Mike, and a 0.11 probability that the dog runs away with the frisbee. Treat this as a 3--state Markov Chain with the dog being an absorbing state. (a) If Mike has the frisbee, what is the expected value for the number of times the frisbee will be thrown before the dog gets the frisbee and runs away with it? (Give your answer correct to 2 decimal places.) times thrown (b) If Mike has the frisbee, what is the expected value for the number of times Mike will throw the frisbee before the dog gets it? (Give your answer correct to 2 decimal places.) times Mike throws
Two dice, one green and one yellow, are rolled. Find the conditional probability. The sum is 12, given that the green one is either 1 or 5 and the yellow one is 1.

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