Practice Exam #2 .13. Given P(l o!) = 0.480. pd)-0.290, and that events l and ar

Question

Practice Exam #2 .13. Given P(l o!) = 0.480. pd)-0.290, and that events l and are disjoint, find Pn. 13. "14. Given P(M and N) = 0.182 and PCM) = 0.282, find PNM) 14. 15. 15. Given P(Q) 0.627, P(R) 0861, and that events Q and R are independent, find PCQ and R). 16. .i6. Given P(U or V) 0.796, Pa)-os86, and Pal and V)-0536, find PO). Given p(Y)-0.309, rZ) 0.315, and that events Yand Z are disjoint, find poor Z). °17. (3 points each) . Show work For questions "18 through 22, sound your answers to three decimal places 18. A charity fundraises by calling a list of prospective donors to ask for pledges. It is able to 18 reach 427%of the people on its list. Of those reached, 323% make apledge. What is the probability that a randomly chosen prospective donor is pledge? reached and the donor makes a Of new motor vehicles sold toindividuals in a recent year, 86.9% were domestic makes or light trucks (where the term, "light trucks" refers to SUVs and minivans), 788% domestic .19-- .19. motor vehicle sold to an individual is a domestic light truck? 20. 20. The probability that steroid test A will detect the presence of steroids in a steroid user is 0.945. The probability that steroid test B will detect the presence of steroids in a steroid user is 0.910. Given that the two tests operate independently of each other, what is the probability that both of them will detect the presence of steroids in a steroid user?

Explanation / Answer

13) Given that : P (I or J) = 0.480 and P(J) = 0.290 Also, I and J are disjoint (mutually exclusive)

So, P(I and J) = 0

Also, P (I or J) = P(I) + P(J) - P(I and J)

0.480 = P(I) + 0.290 - 0

So, P(I) = 0.190

14) Given that : P(M and N) = 0.182 , P(M) = 0.282

P(N given M) = P(N and M)/P(M)

= 0.182/0.282

P(N given M) =0.6454

15) Given that : P(Q) = 0.627 , P(R) = 0.861

Also, Q and R independant events which means;

P(Q and R) = P(Q)P(R)

= 0.627*0.861

P(Q and R) = 0.5398

16) Given that : P(U or V) =0.796 , P(U) =0.586 , P(U and V)=0.536

Also, P(U or V) = P(U) + P(V) - P(U and V)

0.796 = 0.586 + P(V) - 0.536

P(V) = 0.746

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