Suppose we have three events A, B and C such that A and B are conditionally indepen- dent given either C or Cº. The following probabilities are known: • P(C) = 0.15. • P(A|C) = 0.3, P(B|C) = 0.2. P(A|C9 = 0.6, P(B|C®) = 0.4. Answer the following questions: (a) Show whether A and B are independent or not.Calculate (b) P(AU B¶C).

Q: B3. (a) The village of Sunnyridge has installed an array of 6 wind turbines. The probability of any…

A: a) i)To find the probability that the monitored wind turbine operates on any given day, we need to…

Q: 2. If P(A) = 0.3, P(B) = 0.2, and P(AN B) = 0.1, determine the following probabilities: a) P(A') b)…

A: Solution: Given information: P(A)= 0.3 P(B)= 0.2 P(A∩B)= 0.1

Q: A building contractor requires a roll of roofing felt. There are three suppliers in the area and the…

A:

Q: If A and B are two mutually exclusive events with P(A)=0.35 and P(B)=0.55, find the following…

A: Probability quantifies the chances of happening an event. The probability values always lie in the…

Q: There are three events C1, C2, C3 with the probabilities p1, p2, P3 respectively. If /5, and p3 =…

A:

Q: Calculate the following probabilities based on the data of Titanic passengers listed in the table…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: 7. Suppose that an experiment leads to events A, B, and C with the following probabilities: P(A) =…

A:

Q: Consider the following joint probabilities table for X and Y, where a = 1, 2, 3 and y = 1, 2, 3. X\Y…

A:

Q: 2b) Find zo for the following probabilities: Zo ii) P (z ≤ Zo) = 0.30 0.52 0.12 0 -0.52

A:

Q: If two events, A and B, are such that P(A) = 1/6, P(B) = 1/9, and P(An B) = 1/70, find the following…

A:

Q: A letter posted second-class on a Monday has the following probabilities of arriving on Tuesday to…

A: Let's approach this step by step:1) For the first-class letter, the probabilities are as follows:…

Q: Suppose that X ~ N(32, 5). Find the following probabilities. Round to four decimals. а. Р(X 26.5) :

A: Given: μ=32, σ=5  The corresponding z-value needed to be computed: Thus, By using the standard…

Q: Two events A and B have the following probabilities: P (A) = 1/2, P (B)= 3/8, and P (A N B) = 1/4.…

A: For events A and B, it is given that, P(A) = 1/2, P(B) = 3/8, and P(A ∩ B) = 1/4.

Q: 2. Two events A and B are such that P(A)=0.21, P(B) = 0.29, P(A|B)=; 29 Calculate the probabilities…

A: P(A) = 0.21P(B) = 0.29P(A|B) = 829

Q: Two events A and B have probabilities .3 and .5 respectively. It is also known that P(A n Bº) = .2.…

A: As per our guidelines we are suppose to answerthree sub parts.Given,P(A)=0.3P(B)=0.5P(A∩Bc)=0.2

Q: The Venn diagram below shows the probabilities of GMA (X) and ABS-CBN (Y as the best TV network in…

A: We have given that from the venn diagram arr P(X) = 0.28 + 0.15  = 0.43 , P(Y) = 0.34 + 0.15 = 0.49…

Q: 63. For customers purchasing a refrigerator at a cer- tain appliance store, let A be the event that…

A: Concept : P(A|B) = P(A∩B)/P(B) Using this concept, from the given information : P(A) = 0.75 P(A') =…

Q: 16. Let A, B be independent events with P (A) = P (B) = 1/3. Find the probability that neither…

A: Introduction: Independence: Suppose A and B are two events with respective probabilities P (A) and P…

Q: In a village the probabilities of a Bus arriving late 26. when it is raining and when it is not…

A: For the given tree diagram find the missing values I,II and III I = 0.3 ,II = 0.4 ,III = 0.3

Q: Calculate the following probabilities, to two decimal places: If P(A)=0.46, P(B)=0.59, and P(A or…

A:

Q: Q3: b) Ahmed is taking Mathematics and Geology. His probabilities for getting grade of 90 (consider…

A: # Here Given that,     P(M)=0.70     P(G)=0.60     P(M∩G)=0.50

Q: If A and B are independent, with P (A) = 0.6, and P (B) = 0.4, calculate the following…

A: Here it is given that A and B are independent events with P(A)=0.6 and P(B)=0.4.

Q: When an experiment is conducted, one and only one of three mutually exclusive events S₁, S₂, and S₂…

A: From the provided information, P (S1) = 0.4, P (S2) = 0.5, and P (S3) = 0.1 P (A/S1) = 0.4, P (A/S2)…

Q: : Ahmed is taking Mathematics and Seology. His probabilities for getting grade f 90 (consider A =…

A: Solution: Given information: P(Grade of A in mathematics class ) =0.70P( Grade of A in Geology class…

Q: Refer to the tree diagram in Figure 5.7. Suppose  you want to find the probability P(B|A) using the…

A: As per our Q & A guideline, we can answer only three  sub questions.

Q: Q5. An electronic assembly consists of two subsystems A and B. The following probabilities are…

A: Given that, an electronic assembly consists of two subsystems A and B. The following probabilities…

Q: Q2: If P(A)=0.25, P (B) = 0.45, P (ABC)=0.43, draw the Venn diagrams and determine the following…

A: Hi! Thank you for the question. As per the honor code, we are allowed to answer three sub-parts at a…

Q: During the past 6 months, Rebecca has been late to work 20 out of 125 days. Also, during that time,…

A: From the given information, the probability of Rebecca being late to work is 20/125 = 0.16.

Q: A device can fail in four different ways with probabilities T1= 0.5, 12 = 0.1, T3 = 0.1, and 14 =…

A:

Q: Suppose we have a data which includes only two possible events; A and B. If the Events A and B are…

A: A data includes two possible events A and B.

Q: The prior probabilities for events A₁, A₂, and A3 are P(A₂) = 0.20, P(A₂) = 0.50, and P(A3) = 0.30.…

A: LetA1,A2,and A3 are mutually exclusive events and their prior probabilities are given…

Q: Suppose A and B are two events with probabilities: P(A*) = .25, P(B) = .35, P(A N B) = .30. a) What…

A: Given, P(Ac) = 0.25 => P(A) = 1 - P(Ac)  = 1 - 0.25 = 0.75 P(B) = 0.35 P(A ∩ B) = 0.30

Q: The prior probabilities for events Aj and Ag are P(A1) = 0.50 and P(A2) = 0.50. It is also known…

A:

Q: We know that the probability of Taylor Swift dying her hair bright pink is .50. Given that she has…

A: Probability is the chance of occurrence of a favourable event out of all possible outcomes.

Q: The probability that Taylor Swift is Austin’s favorite music artist is .10. The probability that he…

A: Given information, Probability that Taylor Swift is Austin's favorite music artist is 0.1.…

Q: Suppose we know that the probabilities P(A) = .5, P(B|A) = .3 and P(A or B) =.3. What is the value…

A: Given information- We have given the probabilities- P (A) = .5, P (B|A) = .3 and P (A or B) = .3