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Find P(A U (Be UC)9) in each of the following four cases: (a) A, B, and...
1. Find P(AU(B UC)) in each of the following four cases: (a) A, B, and C are disjoint events and P(A) 1/2. (b) P(A)-2P(BC)= 3P(ABC) =1/2 (c) P(A)1/2, P(BC) 1/3, and P(AC)0 d) P(An (Be UC))-0.7
Set operations and probabilities: Find the value of ?(?∪(??∪??)?) for each of the following cases: The events ? , ? , ? are disjoint events and ?(?)=2/5 . ?(?∪(??∪??)?)= ?? The events ? and ? are disjoint, and ?(?)=1/2 and ?(?∩?)=1/4 . ?(?∪(??∪??)?)= ?? ?(??∩(??∪??))=0.7 . ?(?∪(??∪??)?)= ??
Consider the following probabilities: P(AC) 0.57, PB = 0.36, and P(A n B) 0.03 a. Find P(A | BC). (Do not round intermediate calculations. Round your answer to 2 decimal places.) P(A | BC) b. Find P(BC | A). (Do not round intermediate calculations. Round your answer to 3 decimal places.) P(BC A) c. Are A and B independent events? Yes because PAI B = PA) Yes because PAN B)0 No because P(A I B)PA). No because PAN B)0
any help with these problems? 0 2 pts ect Question 13 The addition rule for probability P(A U B) for: p(A) + P(B)-PA n В) is used finding the probability that A happens, then B happens. hinding the probability that A doesn't happen, but B does happen. finding the probability that A or B or both happen 9 inding the probability that A and B both happen Quiz Score: 5.8 out of Question 12 0/ 2 pts The multiplication rule...
2. Prove the following propositions (a) Proposition 1: For every event A, AC A (b) Proposition 2: If A, B, C are events, if A c B and if Bc C, then Ac C (c) Proposition 3: φ-Ω and 0° = φ (d) Proposition 4: If A1, ..Ak (e) Proposition 5: If A and Bare events, then P(A UB)-P(A)+P(B) - P(AB) are disjoint events, then P(UK 1 A.)-Σ'm P(A)
(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,...
Answer the following with TRUE or FALSE, and justify your answer (this does not necessarily have to be a formal prooW). (a) If two events A, B where P(A) > 0, P(B) > 0, P(AN B) > 0 and A, B are independent, then AC and BC are independent as well. (b) For two events A, B where P(A) > 0, P(B) > 0, they can be disjoint and independent at the same time. (c) For two events A1, A2...
Problem 3: If P(A) 0.2, P(B) 0.1, and P(A or B) PIA U B) 0.28, then (a) (2.5 points) find the P(A and B). That is, find P(AnB). (b) (2 points) clearly explain whether the events A, B are mutually exclusive (disjoint). (c) (2 points) clearly explain whether the events A, B are independent based on probability
3. Find the product. a) 3p'(2p +5p)(p +2p+1) b) p(3p+7)(3p-7) c) -(4r-2) d) (2a+3)(a -a' +a-a+ 1)
If x is a binomial random variable, compute p(x) for each of the cases below. a. n=4, x=1, p=0.4 b. n=6, x=3, q=0.6 c. n=3, x=0, p=0.8 d. n=4, x=2, p=0.7 e. n=6, x=3, q=0.4 f. n=3, x=1, p=0.9