M P V:·9PROBLEMS1.pdf >(a) Find the probability that the committee con sists of 2 men and 3 women.(b) Find the probability that the committee consists of all women.Q13A lot of 100 semiconductor chips contains 20 that are defective. Two chips are selected atrandom, without replacement, from the lot.(a) What is the probability that the first one selected is defective?(b) What is the probability that the second one selected is defective given that the first one wasdefective?(c) What is the probability that both are defective?Q14:-Two cards are drawn at random from a deck. Find the probability that both are aces.?Q15Consider the binary communication channel shown in Fig.may assume the state 0 or the state 1, and, similarly, the channel output symhol Y may assumeeither the state 0 or the state 1. Because of the channel noise, an input 0 may convert to anoutput I and vice versa. The channel is characterized by 1the channel transition probabilities p, ,90. P., and q,, defined byThe channel input symbol XPo = P(y, |Xp)40 = P(yo|xandand4; = Ply, [x1)where x, and x, denote the events (X = 0) and (X = 1), respectively, and yo and y, denote theevents (Y = 0) and (Y = 1), respectively. Note that p, + 90 = 1 = p, + q1. Let P(xq) = 0.5, Po =0.1, and p, = 0.2.(a) Find P(yo) and P(y,).(b) If a 0 was observed at the output, what is the probability that a 0 was the input state?(c) If a 1 was obscrved at the output, what is the probability that a 1 was the input state?(d) Calculate the probability of error P,.XQ16In the experiment of throwing two fair dice, let A be the event that the first die is odd, B be theevent that the second die is odd, and C be the event that the sum is odd. Show that events A, B,and C are pairwise independent, but A, B, and C are not independent.II

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Description: M P V:·9PROBLEMS1.pdf >(a) Find the probability that the committee con sists of 2 men and 3 women.(b) Find the probability that the committee consists of all women.Q13A lot of 100 semiconductor chips contains 20 that are defective. Two chips are sel

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Math

Probability

À lot of 100 semiconductor chips contains 20 that are defective. Two chips are selected at random, without replacement, from the lot. (a) What is the probability that the first one selected is defective? (b} What is the probability that the second one selected is defective given that the first one was defective? (c) What is the probability that both are defective?

À lot of 100 semiconductor chips contains 20 that are defective. Two chips are selected at random, without replacement, from the lot. (a) What is the probability that the first one selected is defective? (b} What is the probability that the second one selected is defective given that the first one was defective? (c) What is the probability that both are defective?

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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