3. (Independent Trials). A rifleman hits (H) his target with probability 2/5, and hence misses (M) with probability 3/5. He firesfour times.(i) Write down all the elements of the event A that the man hits the target exactly twice (e.g. the samples MMHH and MHMHbelong to A, but the samples HHHM and MMMH don't) and find P(A).(ii) Assuming independence of shots, find the probability that the man hits the target at least once.For Problem 4, apart from the main table showing the numerical answers to (sub)problems, for each random variable Z underconsideration having the set of values {21, 2,..., ze} and the distribution function f, provide a standard table showing the process ofdetermination of the expected value E(Z) and the expected value E(Z?) of Z?:Zk|| 2122ZeTotalF(2e)zef (ze)zef (ze)f(zk)f(21)Zk f (Zk) 21f(z1) | 2f(22)F(2k) || zif(21) | 3f(22)f(22)As is was discussed in class, whenever all entries in a given table are rational numbers, they can be entered, for convenience's sake, 'asthey are'; otherwise, please round all the entries of the table to 5-digit floating-point numbers.

Answered: 3. (Independent Trials). A rifleman…

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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newspapers. You randomly select 10 U.S. adults. Find the probability that the number of U.S. adults who have very little confidence in newspapers is (a) exactly five, (b) at least sbx, and (c) less 44% of U.S. adults have very little confidence than four. (a) P(5) = (Round to three decimal places as needed.) (b) P(x26) = (Round to three decimal places as needed.) (c) P(x<4) = (Round to three decimal places as needed.)
The PMF of the number of components K of a system that fails is defined by = {( PK (k)= ()(0.2)*(0.8) 4-k k= 0, 1,...,4 otherwise (a) What is the CDF of K? (b) What is the probability that fewer than two components of the system fail?
(a) For two events A and B, suppose that P(A) = 0.3, P(B) = 0.5, and P(AUB) = 0.6. Calculate P(An B). (b) If P(A) = 0.6, P(B) = 0.3, P(An Bc) = 0.4, and BCC, calculate P(AŬBªỤCª).
2. A and B are events such that P(A) = 0.3, P(B) = 0.4, P(A/B) = 0.5. Calculate: (1) P(AB) and P(A + B); (2) P(BA).
3. (Independent Trials). A rifleman hits (H) his target with probability 16/23, and hence misses (M) with probability 7/23. He fires four times. (i) Write down all the elements of the event A that the man hits the target exactly twice (e.g. the samples MMHH and MHMH belong to A, but the samples HHHM and MMMH don't) and find P(A). (ii) Assuming independence of shots, find the probability that the man hits the target at least once.
1. Event A occurs with probability 0.1. Event B occurs with probability 0.6. If A and B are independent, then (а) Р(А or B) %3D 0.70. (b) Р(А or B) 3 0.06. (c) P(A and B) = 0.06. (d) P(A and B) = 0.70.
1. Two events A and B are such that P(A) = 0.5, P(B) = 0.3 and P(AUB) =0ff Calculate P(A B).
(a) P(E) = 0.8, P(F) = 0.5. Suppose E and F are indepdendent.Compute P(E or F) and P(E and F).(b) Suppose that E and F are two events, and P(E) = 0.9 and P(F|E) = 0.3.Compute P(E and F).
If A and B are independent events with P(A)=0.3 and P(B)=0.4. Then P(AB) is
If A and B are two events with P(A) = 2/3, P(B) = 1/5, P(AN B) = 1/15 then Find P(ANB)

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