a) Two events, M and N, are such that P(M) = 0.6, P(M NN) = 0.2, P(M UN) = 0.85FindP(N \M)State, with reason, whether M and N aremutually exclusiveindependent.(i)(ii)(ii1)

Answered: Image /qna-images/answer/4a2ab3d8-2a3e-4c69-82a7-73a9a263fbda.jpg

Answered: a) Two events, M and N, are such that…

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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Events X and Y are such that PP(XX) = 0.30 and PP(XX ∪ YY) = 0.70. Given thatX and Y are independent and non-mutually exclusive, determine PP(YY).
3. Consider the given probablity P(a)=0.7 p(b)=0.8 p(aUb)=o.8 a) Find p(aUb) b) Venn diagram c) Find p(a/b) d) find p'(a'∩ b) e) find (b/a') f) events a and b are
solve a b
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).
(d) P(N and W) P(M and W) (e) P(N or M). Are the events N = no reaction and M = mild reaction mutually exclusive? Explain. No. P(N or M) ≠ 0. No. P(N and M) ≠ 0. Yes. P(N and M) = 0. Yes. P(N or M) = 0. (f) Are the events N = no reaction and W = washing oil off within 5 minutes independent? Explain. No. P(N and W) = P(N) · P(W). Yes. P(N and W) ≠ P(N) · P(W). No. P(N and W) ≠ P(N) · P(W). Yes. P(N and W) = P(N) · P(W).
. If A is an arbitrary event, then show that P(A) = 1- P(A).
7. Given P(A) = 1/3 and P(B) = 1/2 and P(A U B) = 2/3 . . . (d) Find P(BIA) (e) Are events A & B Independent? (f) Are events A & B Mutually exclusive?
3 2 1. Given that P(4)=, P(A/ B)= and P(A/B)=. find : P(ANB) P(B) P(AUB) (а) (i) (ii) (iii) (b) Determine whether the events A and B are : (i) (ii) Mutually exclusive Independent (c) Given that P(A)=0.64 , P(B)=0.36 and P(BnA)= 0.25. Find : (i) P(AOB) (ii) P(AUB) (iii) P(BnA)
(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 two events and P (A) 3 P (B) 5' 2 Then prove that (i) 3 P (A U B) 2 (ii) 10 1
Events A and B are such that P(A) = – P(A/B'y= - and P(A n B)- so P(A/B) is Select one: O a. Ob. O d.
1. (Independence). (i) Recall that given events A, B,C, we have that P(AUBUC) = P(A)+ P(B)+ P(C) – P(An B) – P(AnC)– P(BnC) + P(AN BnC). (4.1) Prove that whenever events A, B,C are mutually independent, we have that P(AUBUC) = 1– P(A^)P(B^)P(C*) = 1– (1– P(A)) · (1 – P(B)) · (1 – P(C)) (and the probability in question can be calculated considerably faster than with the use of the formula (4.1)). (ii) The probability that A hits a target is 2/5, the probability that B hits it is 5/9, and the probability that C hits the target is 3/7. Use (i) to find the probability that the target will be hit if A, B, and C each shoot at the target. (iii) Suppose that the probability that a soldier firing his personal weapon hits an enemy warplane is p > 0. Show then, arguing as in (i), that the probability that the warplane is hit at least once when n > 2 soldiers shoot at it is 1- (1 — р)". (4.2) Evaluate the probability in (4.2) in the case when p = 0.0006 and n = 750, and then round your result to a…

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a) Two events, M and N, are such that P(M) = 0.6, P(M NN) = 0.2, P(M UN) = 0.85 Find P(N \M) State, with reason, whether M and N are mutually exclusive independent. (i) (ii) (iii)