Suppose there are two bins labeled A and B. Bin A contains 3 blue and 9 red balls, and bin Bcontains 4 blue and 4 red balls. Suppose I pick a bin uniformly at random and then draw a balluniformly at random from that bin.(a) What is the probability that I picked bin A given that I drew a red ball?(b) What is the probability that I picked bin A given that I drew a blue ball?

Answered: Image /qna-images/answer/9247dbfb-4fcf-4949-ba18-e430f2d8005c.jpg

Answered: Suppose there are two bins labeled A…

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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Suppose that there is a white urn containing two white balls and three red balls and there is a red urn containing two white balls and four red balls. An experiment consists of selecting at random a ball from the white urn and then (without replacing the first ball) selecting at random a ball from the urn having the color of the first ball. Find the probability that the second ball is red.
Suppose that there is a white urn containing three white balls and one red ball and there is a red urn containing two white balls and four red balls. An experiment consists of selecting at random a ball from the white urn and then (without replacing the first ball) selecting at random a ball from the urn having the color of the first ball. Find the probability that the second ball is red.
Suppose that Bag 1 contains 4 red balls and 2 green balls, and Bag 2 contains 3 red balls and 3 greenballs. You draw two balls at random from Bag 1, and two balls at random from Bag 2.(a) Compute the probability that all four balls drawn are the same colour.(b) Compute the probability that all four balls drawn are green given that all four balls drawn are thesame colour.
8 For this problem, assume there are 3 grey females, 4 grey males, 2 white females, and 3 white males. As in the book, the biologist selects two mice randomly. (1) What is the probability of selecting two males given that both are grey? (2) What is the probability of selecting 1 mouse of each gender given that both are grey?
Airline A is on time 80% of the time, Airline B is on time 85% of the time, and Airline C is on time 90% of the time. Airline A has twice as many flights as Airline B, and Airline B has three times as many flights as Airline C. One flight is selected at random from one of these airlines. (a) What is the probability this flight on time? (b) Given that the flight is on time, what is the probability it is from Airline A?
At a factory that produces pistons for cars, Machine 1 produced 354 satisfactory pistons and 236 unsatisfactory pistons today. Machine 2 produced 560 satisfactory pistons and 140 unsatisfactory pistons today. Suppose that one piston from Machine 1 and one piston from Machine 2 are chosen at random fro today's batch. What is the probability that the piston chosen from Machine 1 is unsatisfactory and the piston chosen from Machine 2 is satisfactory ? Do not round your answer.
Suppose that the population is 1000 people and the probability of cat people is 25% if we take a random sample of 100 people what is the probability that the proportion in the sample will be bigger than 29%
A subcommittee is to be selected from a committee of men and women. For this problem, assume that there are 8 men and 5 women on the committee, and that a subcommittee of 3 is selected at random. What is the probability that all are male given that all are the same sex?
Suppose that there is a white urn containing two white balls and three red balls and there is a red urn containing one white ball and two red balls. An experiment consists of selecting at random a ball from the white urn and then (without replacing the first ball) selecting at random a ball from the urn having the color of the first ball. Find the probability that the second ball is red. The probability of the second ball being red is?

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