13. Suppose E and F are events in a sample space S with P(E) = 0.43, P(F) = 0.69, and P(EUF) = 0.85. Find the following. (a) P(En F) (b) P(E) (c) P(F | E)
Q: 1. P(A) = 0.45, P(B) = 0.25, and P(An B) = 0.35, find the following probabilities: (a) P(A') (b) PA…
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- b. Use the rewritten rule to find P(Z) if P(Y OR Z) = 0.71 and P(Y) = 0.42. 92. G and H are mutually exclusive events. P(G) = 0.5 P(H) = 0.3 a. Explain why the following statement MUST be false: P(H|G) = 0.4. b. Find P(H OR G). c. Are G and H independent or dependent events? Explain in a complete sentence. This OpenStax book is available for free at http://cnx.org/content/col11562/1.18Suppose that we have a sample space S = {E₁, E2, E3, E4, E5, E6, E7], where E₁, E2, ..., E7 denote the sample points. The following probability assignments apply: P(E₁) = 0.20, P(E₂) = 0.05, P(E3) = 0.20, P(E4) = 0.15, P(E5) = 0.25, P(E6) = 0.05, and P(E7) = 0.10. Let A = {E₁, E4, E6} B = {E2, E4, E7} C = {E2, E3, E5, E7}. Find P(AC). 0.7000 0.6000 0.3000 0.5714 O 0.4000 Question 32.3 Let A and B be two events af the same sample space. If A and B are independent and P(A) = 0.5 and P(AN H) = 0.2, then: P(B)
- 1. Two events A and B are such that P(A) = 0.5, P(B) = 0.3 and P(AUB) =0ff Calculate P(A B).Please ASAP, answer all part or left it for other expert7. If an experiment the events A and B can both occur then a. P(A U B) = P(A)P(B|A) b. P(A N B) = P(A)P(A|B) c. P(AN B) = P(A)P(B|A) d. P(A U B) = P(B)P(B|A) %3D
- (a) P(E) = 0.8, P(F) = 0.5. Suppose E and F are indepdendent.Compute P(E or F) and P(E and F).(b) Suppose that E and F are two events, and P(E) = 0.9 and P(F|E) = 0.3.Compute P(E and F).4. Let X be a random variable with values 2, 3, 5, and 6. Find the sampling distribution of the mean of the samples without replacement if n=2. Sample size of Sample Mean Sample Mean x Probability P(x) fQ P.6: On its way, a car meets 4 traffic lights, and the probability that each of them will be red is 0.5. Let X be a discrete random variable equal to the number of traffic lights that were green when the car arrived. X may take the values of 0, 1, 2, 3, 4. (Assume traffic lights are independent.) What is the probability distribution of X? The probability distribution of X is 3 4 p(x) 0.5 0.25 0.125 0.0625 0.0625 The probability of distribution of X is 3 p(x) 0.5 0.5 0.25 0.125 The probability of distribution of X is 3 4 p(x) 0.5 0.25 0.5 0.25 0.125 The probability distribution of X is 1 3 4 p(x) | 0.5 || 0.5 || 0.5 | 0.5 || 0.5 The probability of distribution of X is 3 4 p(x) || 0.0625 0.0625 0.125 0.25 0.5
- Q.6. Use the binomial distribution in which n 6 and p = 0.3 to %3D calculate the following probabilities: (a). X is at most 1. (b). X is at least 2. (c). X is more than 5. (d). X is less than 6.F, G, H, and Y are events in the same sample space with P(A) = 0.26, P(B) = 0.39, and P(C) = 0.18, . F G and H are mutually exclusive. In addition, suppose that P(Y|F) = 0.21, P(Y|G) = 0.43, and P(Y|H) = 0.31. What is the value of P(Y)?