For any two events A and B to be not independent, P(ANB) = P(A).P(B)
Q: Suppose that A, B are two events such that P(A) = 0.7, P (B) = 0.55 and P (A / B) = 0.6 Find P (A…
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Q: Suppose that A and B are independent events such that P(A) = 5/8 and P(B) = 4/7. Find P(A&B).
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Q: Let A and B be two events such that P(A) = 1/7, P(AUB) =1/2, and P(AB) =1/2 Determine P(B)
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Q: It is known that P(AB)=0.45, P(B)=0.90 and the events A and B are independent. Find…
A: Independent events are events that do not affect the outcome of subsequent events.
Q: If A and B are events such that P(A)equals=0.60 and P(A∪B)equals=0.70, find P(B) when (a) A…
A: (a)If events A and B are mutually exclusive events, then, P (A or B) = P(A)+ P(B).Or, P(B) = P (A or…
Q: Example 2.3.11 Show that for any two events A and B, P(AN B) s P(A) s P(A U B) s P(A) + P(B) nned…
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Q: Let A and B be two events such that p(A) = 0.4 and P(BA) = 0.2. Then P(BnA) = 0.4 0.7 0.6 0.5
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Q: A and B are independent events. If Pr[A]=0.5 and Pr[B]=0.7, what is Pr[A∩B′]?
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Q: If A and B are mutually exclusive events with P(A) = 0.295, P(B) = 0.32, then P(A | B) =
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Q: Suppose that A and B are mutually exclusive events such that P(A) = 0.25 and P(B) = 0.40. Determine…
A: Special Addition Rule:
Q: Q2. Two events A and B are said to be dependent if and only if:
A: Here use basic of dependent events
Q: - For any two events A and B; P ( ACO B) =P (B)-P (AOB)
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Q: A and B are independent events. If Pr(A intersect B)= 0.32 and Pr[A]= 0.4 what is Pr [B]?
A: Given Data: The probability of A intersect B is: PrA∩B=0.32 The probability of A is: PrA=0.4 Event A…
Q: Suppose P(A) = 0.28 and P(B) = 0.48 and A and B are independent. Events A and B are not disjoint.…
A: Answer is mentioned below
Q: The rule P (E U F) = P (E) + P (F) - P (EN F) is used for: * all events disjoint events O Any two…
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Q: (a) Two independent events, A and B, are such that, P(A) = 0.7 and P(B) = 0.4, calculate: (i) P(An…
A: We have to solve given problem:
Q: For two events A and B , P(A)=0.7 , P(B)=0.4 , and P(A∩B)=0.28. Determine whether or not A and B are…
A: Given that P(A)=0.7 , P(B)=0.4 , and P(A∩B)=0.28
Q: Let A and B be two events such that P(A) = 1/6 While P(A or B) = 1/2. Let P(B) = P. For what values…
A: P(A or B)= P(A)+P(B)-P(A and B) For A and B to be independent P(A and B)=P(A).P(B) Therefore, P(A or…
Q: Suppose that A, B are two independent events, with P(A) = .1 and P(B) = .2. Find P(A|B).
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Q: For any two events A and B; P (AUB) = P (A) + P (B) – P ( A nB) %3D
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Q: Can two events A and B be independent of one another and disjoint? Explain what conditions are…
A: Two events are independent, if the occurrence of one does not change the probability of the other…
Q: Let A and B be two events such that P (A) = 0.46 and P (B) = 0.07 (a) Determine P (A ∪ B), given…
A: Given: A and B be two events such that P (A) = 0.46 P (B) = 0.07
Q: For this problem, assume that Pr[A∪B]=0.55Pr[A∪B]=0.55 and Pr[A]=0.25Pr[A]=0.25. (1) What is…
A: P(A or B) =0.55 and P(A) =0.25. Events A and B are independent.
Q: If A and B are events such that P(A)=0.2 and P(A∪B)=0.4, find P(B) when (a) A and B are…
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Q: Let A and B be two events such that P(A)=1/7, P(AUB)=1/2, and P(AB)=1/12. Determine P(B)
A: From the provided information, P (A) =1/7 P (A Ս B) = 1/2 And P (AB) = 1/12
Q: A and B are independent events. If Pr(A∩B)=0.4 and Pr[A]=0.5 what is Pr[B]Pr[B]?
A: It is given that, P(A)=0.5, P(A and B)=0.4.
Q: A and B are independent events. If Pr[A]=0.3 and Pr[B]=0.5, what is Pr[A∩B′]?
A: Since the events A and B are independent, the events A and are also independent.
Q: Let A and B be two events such that P(A)=0.5, and the probability that neither occurs is 0.3. Find…
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Q: If A and B are two events such that P(A) = 0.3 and P(B) = 0.6, then P(A|B) = ____
A: We have given that, A and B are two events and P(A) = 0.3 and P(B) = 0.6, then, We will find P(A|B)…
Q: Let X and Y be the two possible events of an experiment where, p(X) = 0.5, (XUY) = 0.9 and p(Y) = p.…
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Q: A and B are events such that P(A)=0.75 and P(B)=0.16 Find mutually exclusive P(A\B)
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Q: A and B are independent events. If Pr(A n B) = 0.16 and Pr[A] = 0.2 what is Pr[B]?
A: If A and B are two independent events then:
Q: Let A and B be two events such that P (A ∪ B) = 0.6 and P (A ∪ Bc ) = 0.8 Find P (A).
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Q: Suppose that C and D are mutually exclusive events such that P(C) = 0.14 and P(D) = 0.32. Determine…
A: Given, P(C) = 0.14 P(D) = 0.32 P(C or D)=?
Q: If two events A and B are not mutually exclusive, then P(A U B) can be computed by the formula P(A U…
A: Given that A and B are not mutually exclusive. So it will roughly look like:
Q: J A and B are independent events, prove that the events A and B,A and B; and A and B are also…
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Q: 48. Can two events A andB be independent of one another and disjoint? Explain what conditions are…
A: Let A and B two events. A and B are said to be disjoint if PA∩B=0. A and B are independent if…
Q: For this problem, assume that Pr[A∪B]=0.85 and Pr[A]=0.5Pr[A]=0.5. What is Pr[B] if A and B are…
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Q: For two events A and B, suppose P(A)=0.6, P(B)=0.2, and P(A|B)=0.7, then P(A U B)= __________.…
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Q: P(A) + P(B) = 1 for any events A and B that are mutually exclusive. True False
A: We have given that, P(A) + P(B) = 1 for any events A and B that are mutually exclusive ? Then, We…
Q: Let A and B be events such that 0
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Q: Let A and B be two events such that P(A) = 1/6 While P(A or B) = 3/8. Let P(B) = P. For what values…
A: Given data, P(A) = 1/6 P(A or B) = 3/8 P(B) = P p=?
Q: Show that for two events A and B, any P(A N B) s P(A) s P(A U B) s P(A) + P(B)
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Q: Show that for any events A and B, P (A ∩ B) ∪ (A ∩ B) = P(A) + P(B) − 2P(A ∩ B)
A: Given : A and B be the any events
Q: suppose two events A and B are independent, with P(A) = 0 and P(B) = 0. by working through the steps…
A: 1) Condition for Independence: If A and B are independent events, then P(A and B)=P(A)*P(B).…
Q: Two events F1 and F2 are said to be mutually exclusive if F1u F2 o
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- Fast pls solve this question correctly in 5 min pls I will give u like for sure Sini T coins are dropped to the lear ploor. If at leacts 5 of them tre heods what is the probablity all 7 ate heads? 7 coins are dropped to the ploor, if at least 3 of them are heads wat is the probability all 7 are neads?An urn contains 10 balls: 4 red and 6 blue. A second urn con- tains 16 red balls and an unknown number of blue balls. A sin- gle ball is drawn from each urn. The probability that both balls are the same color is 0.44. Calculate the number of blue balls in the second urn. Choose one of the following. Source: Society of Actuaries. a. 4 b. 20 c. 24 d. 44 e. 64Your internal body temperature T in °F is a Gaussian (μ =98.6, σ = 0.4) random variable. In terms of the Φ function, find P[T > 100]. Does this model seem reasonable?
- A life insurance salesman operates on the premise that the probability that a man reaching his sixtieth birthday will not live to his sixty-first birthday is 0.050.05. On visiting a holiday resort for seniors, he sells 1010 policies to men approaching their sixtieth birthdays. Each policy comes into effect on the birthday of the insured, and pays a fixed sum on death. All 1010 policies can be assumed to be mutually independent. Provide answers to the following to 3 decimal places.Part a)What is the expected number of policies that will pay out before the insured parties have reached age 61?Part b)What is the variance of the number of policies that will pay out before the insured parties have reached age 61?Part c)What is the probability that at least two policies will pay out before the insured parties have reached age 61?Let X and Y be random variables, and a and b be constants. ???? a) Show that Cov [aX,bY] = abCov [X,Y] . b) Show that if a > 0 and b > 0, then the correlation coefficient between aX and bY is the same as the correlation coefficient between X and Y . c) Is the correlation coefficient between X and Y unaffected by changes in the units of X and Y ?Everyday, James reverses his car from his driveway on to the road in such a way that there is a very small probability P that his car will be involved in a collision. ( i) Show that the probability that there will be no collision in a five-day week is (1−P)^5 and state one assumption that is made in your answer. (iii) Let P = 0.001. Check that the Poisson approximation can be used, and find the approximate probability that James will avoid a collision in 500 days.
- Solve the Fourier series of f(x) = (a+b)x -π < x < πwhere a and b are the first and second digit of your roll number respectively roll no is 070-What is the probability of obtaining a z value less than 1.3? -What is the probability of obtaining a z value more than 1.75? -What is the probability of obtaining a z value between -2 and -1.35? -Find the value of z such that the area to the left of z is 0.8178. -Find the value of z such that the area to the right of z is 0.0305. -What is the value of z0 if P(z ≤ z0) = 0.1507? -What is the value of z if the area between -z and z is 0.74?A company that manufactures medical devices is conducting tests in R&D on a new product. The product is in production on a pilot run (product will not be sold from the pilot run). The product is manufactured in batches and the quality of the batch must be determined, by testing a sample of 9 devices selected at random from a batch. One aspect that is monitored is the width of the bond in the device, ideally this should be equal to 3 mm on average. A sample from the latest batch gave the following bond widths measured in mm: 3.2, 2.8, 2.7, 3.0, 2.9, 2.9, 2.9, 3.2, 2.8 these gave an average of 2.93 mm and the widths varied by a standard deviation of s = 0.17 mm. Test, at significance level α = 0.01, whether there is evidence that the average bond width of the batch of devices is different to the required specification, by testing the following hypotheses: H 0: μ = 3 mm H a: μ ≠ 3 mm. Complete the test by filling in the blanks in the following:An estimate of the population mean is…