Example 3: Given that P(A) = 0.17, P(B) = 0.22, P(A or B) = 0.33: (a) Compute P(A and B). (b) Are the two events mutually exclusive? Explain. (c) Are these two events independent of each other? Explain?
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We know,
P(A)=0.17, P(B)=0.22 and P(A or B) =0.33
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- A and B are mutually exclusive events. P(A) = 0.30 and P(B) = 0.50. What is P(A or B)? A. 0.80 O B. 0.20 ) 5 C. 015 OD. 0.60 OOOIdentify why this assignment of probabilities cannot be legitimate: P(A) = 0.4, P(B) = 0.3, and P(A and B)=0.5 (A) A and B are not given as disjoint events (B) A and B are given as independent events (C) P(A and B) cannot be greater than either P(A) or P(B) (D) The assignment is legitimateE and F are mutually exclusive events. P (E) = 0.91; P(F) =0.42 . Find P (E| F )
- Classify the events as independent or not independent. Events A and B where P(A) = 0.6, P(B) = 0.9, and P(A and B) = 0.54 Select one: a.independent b.not independentU and V are mutually exclusive events. P(U) = 0.27; P(V) = 0.59. Find: a. P(U and V) = ______ b. P(U|V)= _______ c. P(U or V)= ________For each set of probabilities, determine whether the events A and B are independent or dependent. (If necessary, consult a list of formulas.) Probabilities Independent Dependent = P(A 18) - 1 (a) P(A)=-;P(B) =;P(A\B) = 5 1 1 P(A) =;P (B) = P(A and B) = %3D 4 6. 1 1 P (B|A) = 1 (c) P(4)-극: P(B)-P(Bl4): %3D %3D 1 1 (d) P(A) = : P(B) = P(4 |B) = | %3D
- Suppose that events A and B are mutually exclusive with P(A) = 1 2 and P(B) = 1 6 . (Enter your answers as fractions.) (a) Are A and B independent events? Explain how you know. Since the events are mutually exclusive we know P(A|B) = which P(A) and thus the events are . (b) Are A and B complementary events? Explain how you know. We know that P(A) + P(B) = . And, since P(A) + P(B) 1, the events A and B complementary events.K Suppose Emerson wins 41% of all checker games. (a) What is the probability that Emerson wins two checker games in a row? (b) What is the probability that Emerson wins three checker games in a row? (c) When events are independent, their complements are independent as well. Use this result to determine the probability that Emerson wins three checker games in a row, but does not win four in a row. (a) The probability that Emerson wins two checker games in a row is (Round to four decimal places as needed.) (...)