Prove that if E1, E2,.., En are independent events, then P(E, U E2 U .. U En) = 1- | 1– P(E;)] i=1

Q: Suppose that E and F are two events and that N(E and F) = 470 and N(E) = 570. What is P(F|E)? .....…

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Q: According to special rule of addition P(A or B) = P(A) + P(B), is true if and only if a.A and B are…

A: We need to find the special rule of addition for which P(A or B) = P(A) + P(B) is true .

Q: Which of the following is NOT necessarily true for mutually exclusive events A and B? P(A B)=0…

A: If A and B are mutually exclusive events, then A∩B=∅. Then, we have P(A∩B)=P(AB)=0. 1.)…

Q: 5. A and B are two events such that P(B) = P(An B) =and P(B|A) = Find a) P(A) b) P(A|B) c) P(A|B)

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Q: a. Let A and B be two events such that P(A) = 0.05 and P(A U B) = 0,49. Calculate P(B') if events A…

A: Continue with Simple probability theory...............

Q: a) Two events, A and B, are such that P(A U B) = 0.86, P(B) = 0.72 and P(A) = 0.64. Determine (i) P…

A: P(A∪B)=0.86P(B) = 0.72P(A) = 0.64

Q: 3. A and B are events such that P(A) = 0.2 and P(A U B) = 0.5. Find P(B) in each of the following…

A: There are two events A and B are given.The given probabilities are as follows

Q: Suppose that A and B are independent events such that P(B) = 0.70 and P (B)=0.20. Find P(An B) and P…

A: Given thatA and B are independent events.such that

Q: Suppose that  A  and  B  are independent events such that  =PA0.10  and  =PB0.70 . Find  P∩AB  and…

A: From the provided information,P (A) = 0.10P (B) = 0.70The events A and B are independent.

Q: . If P(A n B) = P(A U B) = and P(A) =;, then A A and B are independent events B A and B are mutually…

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Q: Question 10 Events A and B are such that P(An B) = 1, P(B|A) = and 10 P(A' B') = a) Find i) P(A) ii)…

A: P(A and B)=1/10, P(B|A)=1/4, P(A' and B')=1/5

Q: (iiven that A and B are two independent events such thatP(1) = 46. andP(A U B) P(B) = 10 2 13

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Q: Let A and B two events and disjoint. Find P(A°U B') اختر احدى الدجابات 1- P(An B) O None 1- P(AU B)

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Q: Let A and B be independent events with P(A) = P(An B) = P(AUB) = 1 ·|6 1 and P(B) = Find P(An B) and…

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Q: Assume A and B are independent events with P(A) = 0.1 and P(B) = 0.3. Find (a) P(A N B), (b) P(A U…

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Q: Let A and B be events such that P(A) =1/8, P(A or B)=1/6 and P(A and B)=1/11. Determine P(B)

A: P(A) =1/8, P(A or B)=1/6,  P(A and B)=1/11.

Q: Show that if A and B, (n = 1,2,3, . -) are events, then An (U Bn) = U (AN Bm)

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Q: Show that if E1,... , En are events such that P(E;) = 1 for i = 1, ...,n, then Ek) = 1. k=1

A: We have events E1, E2,...., En such that PEi = 1. We have to that the probability of the event…

Q: Let A and B be events such that P(A)=1/4, P(A or B)=1/3, and P(A and B)=1/5. DetermineP(B)

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Q: Suppose that events F and S are conditional independent events given D and -D respectively with…

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Q: Suppose that A and B are events such that P (A|B) = P (B|A) , P(AUB) = 1, and P(An B) > 0. Prove…

A: Solution: From the given information,

Q: Two events A and B are such that P(A)=1/4, P(A/B)=1/2, and P(B/A)=2/3. 1) Are A and B independent…

A: Using P(B|A)=23 and the conditional probability formula we…

Q: a) Show that for any three events A, B, and C, the probability that at least one of them occurs is…

A: Given  We need to prove that for three events A,B and C,the probability that atleast one of them…

Q: 8. Let A, B and C be three events such that P(BOC) > 0. Prove or disprove each of the following…

A: a) P(An BC) = P(A|BC)P(BC) is actually true. This can be proven using the conditional probability…

Q: Complete the following table and use it calculate the probabilities given below. A AC Total a. PA or…

A: Given data is:   B Bc Total A 0.443 0.218   Ac       Total 0.567   1

Q: 88) Suppose that the probability of rain today depends on weather conditions from the previous three…

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Q: Question 1. Suppose A and B are events with P(A) = ½, P(B) and 113 P(A or B) = a) Are A and B…

A: Given that  P(A) = 1/3 , P(B) = 1/4 , P(A or B) = 1/2

Q: Bayes' theorem for an 'AND’ combined event is: Pr( A 'AND' B) = Pr( A|B )*Pr( B ). When does this…

A: We have given the following statement about the  Bayes  theorem.

Q: Let A and B be two events such that P(A) = ¼ While P(A or B) = ½. Let P(B) = P. For which value of…

A: The probability of happening of event A is 14. The probability of happening of event A or event B…

Q: 2. Let 0 0, P(B| A) = P(B|A), then that event A and B are independent. prove

A: We need to prove, P(AnB) = P(A)P(B)

Q: 3. Let C and D be events with P(C) = 0.1, P(D) = 0.6, and P(C U D) Are C and D independent? Explain.

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Q: If P(E) = 0.2, P(F) = 0.3, and E and F are independent events, find P(E and F). 1) 0.06 2) 0.08 3)…

A: P(E)=0.2P(F)=0.3and E,F are independent events.

Q: Suppose that A and B are two independent events for which P(A)=0.32 and P(B)=0.7. Find each of the…

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Q: 3. Two events A and B are such that P (A) = 0.6, P (B) = 0.4 and P(A/B) = 0.2 Find a) P(ANB) b)…

A: it is given that  P(A) = 0.6 P(B) = 0.4 P( A/B ) = 0.2   Note: According to Bartleby expert…

Q: Choose the following statements that are true for any events A, B. Pr{AU B} = Pr{A} + Pr{B} –…

A: Answer - Choose the following statements that are true for any events A, B.

Q: Let A and B be events. Assume that P(A) = 0.55, P(B|A) = 0.36, and P(B|A') = 0.84. Then, P(A∩B)=?,…

A: P(A) = 0.55P(B|A) = 0.36P(B|A') = 0.84