

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...
Let B and C be two events such P (B) = 0.12 and P (C) = 0.52. Do not round your responses. (If necessary, consult a list of formulas.) (a) Determine P (B ∪ C) , given that B and C are mutually exclusive. (b) Determine P (B ∪ C) , given that B and C are independent. Thank you
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)
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.
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