2. (a) There are 12 identical balls and 5 distinct containers: A, B, C, D and E. In a random experiment, the 12 balls are randomly put into the 5 containers, with at least one ball in container A but no restrictions on the number of balls in the other containers. Let X be the number of empty containers at the end of the experiment. Find its probability distribution function and the expected number of empty containers. Note: Here we assume that every configuration is equally probable. (b) There are three containers, A, B and C. Each container contains 25 balls, which are either red or blue. Container A has 15 red balls, container B has 16 red balls, and container C has 12 red balls. In a random experiment, one first randomly chooses a container, and then a ball is drawn from the chosen container. The probability of choosing container B in step 1 is 25 . The experiment is designed so that the events "the ball drawn is red" and “the ball drawn comes from container A" are independent. Suppose that the ball drawn is red. What is the probability that it came from container C?

2. (a) There are 12 identical balls and 5 distinct containers: A, B, C, D and E. In a random experiment, the 12 balls are randomly put into the 5 containers, with at least one ball in container A but no restrictions on the number of balls in the other containers. Let X be the number of empty containers at the end of the experiment. Find its probability distribution function and the expected number of empty containers. Note: Here we assume that every configuration is equally probable. (b) There are three containers, A, B and C. Each container contains 25 balls, which are either red or blue. Container A has 15 red balls, container B has 16 red balls, and container C has 12 red balls. In a random experiment, one first randomly chooses a container, and then a ball is drawn from the chosen container. The probability of choosing container B in step 1 is 25 . The experiment is designed so that the events "the ball drawn is red" and “the ball drawn comes from container A" are independent. Suppose that the ball drawn is red. What is the probability that it came from container C?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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