#5 (4 pts.) Consider the following sample space S and events A and B. s-(-4 <...
5. Consider an experiment with sample space S and events A,B,C, and D with the following probabil ities: P(AUB)-|, P(A) = P(čnD) = , P(C) = 훙 Furthermore, A and B are mutually exclusive (ie. A กั-o), while C and D are independent (ie. P(cr D) = P(C)P(D)). (Note: I know this looks like a lot of parts, but these are all short, quick answers!) (a) Find P(An (b) Find P(B) (c) Find P(AnB) (d) Find P(AUB) (e) Are A...
Question 11 5 pts Let A, B and C be three non-empty events defined on a sample space 12. Furthermore, suppose that • B and Care mutually exclusive, • A and B are independent and • A and C are independent. Show that P (BUC | A) = P (BUC)
Consider an experiment with sample space S and events A,B,C, and D with the following probabl ities: P(AUB)-, P(A)- , P(Cn D) , PC)- . Furthermore, A and B are mutually exclusive (i.e. AnB-), while C and D are independent (i.e. P(CND) P(C)P(D)). Note: I know this looks like a lot of parts, but these are all short, quick answers!) ' (a) Find P(AnB (b) Find P(B) (c) Find P(A กั Bc). (d) Find P(AUBe) (e) Are A and B...
In a sample space, events A and B are independent, events B and C are mutually exclusive, and A and C are independent. a) Show that P(AUB) = P(B) + P(A)P(B') = P(A) + P(A')P(B) b) If P(AUBUC) = 0.9, P(B) = 0.5 and P(C) = 0.3 find P(A).
Question 1 1 pts Suppose A and B are mutually exclusive events in a sample space S with probabilities P(A) - 0.22 and P(B) = 0.39 respectively. What is the probability that either A or B occurs? (Round the value to the 2-nd decimal place) 0.39 0.61 0.0 Not enough information to answer the question 0.48 0.52 O 0.70
Problem 1.2 Consider an experiment with sample space S = {1,2,3,4}. Define events A, B, C as A = {1,2}, B = {2,3}, C = {1,4}. (a) Are A, B, C mutually disjoint? Are A, B, C collectively exhaustive? (b) Is it possible to have P[A] + P[B] + P[C] = 1? Explain why or why not. (c) If P[A] + P[B] + PIC] = 1, what is the value of P[A]?
2. Let A and B be events in a sample space such that P(A) -0.5. P(ANB) -0.3 and PLAUB)=0.8. Calculate: 1) P(AB): ii) P(BA): iii) PIBIA B): be independent of A and such that B and Care Let the event C in mutually exclusive. Calculate: iv) P(AC); v) PIANBNC). (8 Marks)
Consider the sample space S = {-3,-1, 0, 2, 4} and the events A = {-1, 0}, B = {0, 2}, and C = {-3, 0, 4} derived from the discrete random variable X. Let the probability of each outcome be as listed in the table below. Outcome (X) Probability −3 0.10 −1 0.20 0 0.30 2 c 4 0.25 Outcome (X) l Probability -3 0.10 -1 0.20 0 0.30 2 c 4 0.25 a) Find the value of the...
(7) The events A and B are mutually exclusive (disjoint). If P(A) = 0.7 and P(B) = 0.2, what is P(A or B)? A) 0.14 B) 0 C) 0.9 D) 0.5 (8) The events A and B are mutually exclusive (disjoint). If P(A) = 0.2 and P(B) = 0.1, what is P(A and B)? A) 0.02 B) 0 C) 0.5 D) 0.3 (9) A probability experiment is conducted in which the sample space of the experiment is S = {1,...
Problem #3: Let A and B be two events on the sample space S. Then show that a. P(B) P(AOB)+P(AnB) b. If Bc A, then show that P(A)2 P(B) Show that P(A| B)=1-P(A|B) C. P(A) d. If A and B are mutually exclusive events then show that P(A| AUB) = PA)+P(B) Problem 4: If A and B are independent events then show that A and B are independent. If A and B are independent then show that A and B...