Here 3P(B and C) = x, hence P(B and C) = x/3
also, P(A and B and C) = 0 as A is mutually exclusive to both B and C
4. Suppose A, B, C are events such that P(A), P(B), P(C) a. If (A, B, C) are independent, show that P(AU BUC)- b. If A, B, C are only pairwise independent, show that 17 24 SHA UBUC)<19 24
A 0.2 В 0.5 0.1 Given the events A and B above, find the following probabilities P(A and B) P(A or B) P(A | B) P(B | A) = P( not A and B) = P(A and not B) Are events A and B independent (yes Explain why or why not or no) Are events A and B independent (yes Explain why or why not or no) GRB 5/5/2019 Math 121 Final Spring 2019
(a) Are following claims correct? Why / Why not? (i) If two events A and B satisfy P(A) > 0.5 and P(B) > 0.5 then An B=ø. (ii) If two events A and B satisfy P(A) >0 and P(B) <1 and ACB then A and B are dependent. (b) Let A and B be two independent events, show that A and B are independent. Are A, B also independent?
Given the following information about events A, B, and C, determine which pairs of events, if any, are independent and which pairs and mutually exclusive. P(A)=0.02 P(A|B)=0 P(B)=0.02 P(C|B)=0.15 P(C)=0.15 P(A|C)=0.02
2. Using the below table: A A2 0.3 В В 0.4 0.2 0.1 08 a. Compute P(A; or B1). b. Compute P(A) or B2) c. Calculate the marginal probabilities from the following table of joint probabilities. d. Detemine P(A | B1). e. Determine P(A2 B1). f. Did your answers to parts (a) and (b) sum to 1? Is this a coincidence? Explain. g. Calculate P(A; | B2) h. Calculate P(A2| B1). i. Are the events independent? Explain. bivong slde glT8...
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 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)
Given the following information about events A, B, and C, determine which pairs of events, if any, are independent and which pairs and mutually exclusive. P(A)=0.78 P(B)=0.34 PC) -0.21 P(BA) =0.78 P(CB) =0.21 PAC) =0.21 Elect all that apply: O A and C are independent O A and B are independent O A and B are mutually exclusive OB and C are independent
You are given the following information about the events A, B, and C. • P(A) = 0.45 • P(B) = 0.50 • P(C) = 0.40 • P(A and B) = 0.2250 • P(B and C) = 0.1732 • P(A and C) = 0.1572 Determine which (if any) pairs of the three events are independent.
Show all work Section 2.4 13. Use the accompanying diagram to determine the probabilities: a) P(Bº) b) P(A) c) PIA UBUC) d) P[ A C ] e) P[AUB] f) P[ CA] .02 .13 i) P[COBOA] 8) P[CUB] h) P[(AUB) I j) P[(89)°7 k) P[(AUBUC) ) P[A – B] m) P[A-(BUC] n) P[A-(BAC 14. Two events, A and B, are such that P(A)=.45,P(B) = 65,P( A B)=.25, determine P(AUB). 15. Two events, A and B, are such that P(A)=.45,P(B)=.65,P(AUB)= 7, determine...