a) Given events A, B, and C with their respective probabilities, P(A) = 0.30, P(B) = 0.40 and P(C) = 0.50. Assume that A and B are mutually exclusive events and A and C are independent events, and P(BIC) = 0.10. Find P(A U BUC).
Q: If P(A) > 0, P(B) > 0, and P(A n B) = 0, then the events A and B are independent. true or false?
A: Solution-: If P(A) >0, P(B)>0 and P(A∩B)=0, then the events A and B are independent. We find…
Q: The prior probabilities of events A1, A2 and A3 if P(A1)=0.20, P(A2)=0.50 and P(A3)=0.30. The…
A: Given that , P(A1) = 0.20P(A2) = 0.50P(A3) = 0.300.500.400.30
Q: Suppose among a population of students 50% own a laptop and 30% of the total have a laptop but no…
A: Answer:- Given information is, P( laptop) = 50% = 0.50 P( laptop and no tablet) = 30% = 0.30 P(…
Q: Mary and Susan are each to play a tennis match. Let the probability that Mary wins her match be 0.65…
A:
Q: Assume that we have two events A and B, that are mutually exclusive. Assume further that P(A) = 0.35…
A: Two event called mutually exclusive if p(a and b)=0
Q: Given two events G and H, the probabilities of each occurring are as follows: P(G) = 0.35; P(H) =…
A: First question: For an non null event A it known that P(A) + P(Ac) = 1.
Q: Let V be the event that a computer contains a virus, and let W be the event that a computer contains…
A: Given Data: P(V)=0.12 P(W)=0.63 P( V and W)=0.04
Q: If A and B are any two events with P(A) =.8 and P(B|A) = 0.4, then the probability of A and B is?
A:
Q: We know that on a random day during the summer the probability that the student jogs is 0.65, the…
A: Let J - jogs, S-swim. P(J) = 0.65 P(S) =0.40 P(J and S) = 0.18
Q: Determine if events A and B are independent: P(A) = 0.5 P(B) = 0.7 P(A U B)= 0.85
A:
Q: Given events J and K: P(J) = 0.28; P(K) = 0.47; P(J or K) = 0.65 Find P(J and K). Find the…
A: Given information- We have given two events J and K. P(J) = 0.28; P(K) = 0.47; P(J or K) = 0.65 We…
Q: You are given two events C and B. You want to determine if the events are mutually exclusive…
A: Determine whether the events C and B are mutually exclusive or not. The correct option is…
Q: Consider two disjoint or mutually exclusive events A and B. If P(A)=0.7 and P(B)=0.2 find P(A or B)
A: Given P(A)=0.7 and P(B)=0.2 A and B are mutually exclusive
Q: If A and B are any two events with P(A) = 0.9 and P(B|A) = 0.5, then the probability of A and B is?
A:
Q: 4. P4 = P(A | Bº). (P1, P2, P3, P4) =(
A: From the given information we have P(B) = 47/210 P(Bc) = 1 - P(B) = 1 - 47/210 = 163/210
Q: U and V are mutually exclusive events. P(U) = 0.29; P(V) = 0.49. Find: a. P(U and V) = b. P(U|V)= c.…
A: The given probabilities are PU=0.29;PV=0.49. And also events U and V are mutually exclusive events.
Q: One girl and one boy One girl who is left-handed and one boy who is left-handed. Two left- handed…
A: 1)Probablity of choosing one girl and one boy :The number of way to choose girl out of and boy…
Q: For events A, B, and C, we have the following probabilities: P(A) 0.7, P(B) = 0.5, P(C) = 0.3, P(A…
A:
Q: A car can travel from Town A to Town C by using the four roads below. The probabilities of these…
A: the probability that a car cannot reach Town C from Town A = P(H1) * P(H2) * P(H3) * P(H4)
Q: Suppose that A,B, & C are three independent events such that Pr(A)=1/4, Pr(B)=1/3, and Pr(C)=1/2. A.…
A:
Q: Suppose P(A) = 0.2 and P(B) = 0.35, and P(A or B) = 0.48, for two events A and B. What is the…
A:
Q: The events A and B are mutually exclusive. If P(A) = .33 and P ( B) = .26, what is the P( A or B)
A: Given that P(A) = .33 and P ( B) = .26
Q: If events C and D are mutually exclusive, then P(C and D) = A. 1 B. 0 C. .50 D. the sum of the…
A: Given data is The events C and D are mutually exclusive
Q: Suppose E and F are two possible events that are independent of one another. Would it be true that…
A: GIVEN DATA : E and F events are independent of one another. TO SHOW : The complements of E &…
Q: A and B are independent events. P(A) = 0.50 and P(B) = 0.30. What is P(A and B)? O A. 0.015 B. 0.15…
A: Given
Q: Let's say (B₁, B₂, B3, B4, B5) is a collection of events that are mutually exclusive events. If…
A: Two events are said to be mutually exclusive if both of them cannot occur at the same time. Two…
Q: The events A and B are mutually exclusive. If P(A) = .31 and P ( B) = .42, what is the P( A or B)
A: It is given that P(A) = 0.31 P(B) = 0.42
Q: Suppose that, for events A and B, P(A)= 0.2, P(B)= 0.85, and P(AandB)= 0.17. Are A and B…
A:
Q: A students is going to graduate from a business department of a university by the end of the…
A:
Q: Given two events G and H, the probabilities of each occurring are as follows: P(G) = 0.5; P(H) =…
A: Given,P(G)=0.5P(H)=0.31P(H AND G)=0.09
Q: Customers at a gas station pay with credit card (A), debit card (B), and cash (C). Assume each…
A: Given: Customers at a gas station pay with credit card (A), debit card (B), and cash (C). P(A) =…
Q: If P(A∪B)=0.6, P(A)=0.4, and P(A∩B)=0.25, find P(B). Assume that A and B are events.…
A: GivenA and B are eventsP(A∪B)=0.6P(A)=0.4P(A∩B)=0.25
Q: Let A and B be independent events. Express the probability P(A ∪ B) in terms of the…
A: Given, A & B are independent events.
Q: The events A and B are mutually exclusive. If P(A)=0.6 and P(B)=0.2, what is P(A or B)?
A:
Q: If event A and event B are mutually exclusive, and P(A) = 0.5 and P(B) = 0.3, find P(A and B).
A: From given data we have : P(A)=0.5 P(B)=0.3
Step by step
Solved in 2 steps with 2 images
- Two events A and B have the following probabilities: P (A) = 0.4, P (B)= 0.5, and P (A and B) = 0.3. Find P( B and AC).The prior probabilities for events A1, A2, and A3 are P(A1) = 0.20, P(A2) = 0.30, and P(A3) = 0.50. The conditional probabilities of event B given A1, A2, and A3 are P(B | A1) = 0.50, P(B | A2) = 0.30, and P(B | A3) = 0.40. (Assume that A1, A2, and A3 are mutually exclusive events whose union is the entire sample space.) (a) Compute P(B ∩ A1), P(B ∩ A2), and P(B ∩ A3). P(B ∩ A1) = P(B ∩ A2) = P(B ∩ A3) = (b) Apply Bayes' theorem, P(Ai | B) = P(Ai)P(B | Ai) P(A1)P(B | A1) + P(A2)P(B | A2) + + P(An)P(B | An) , to compute the posterior probability P(A2 | B). (Round your answer to two decimal places.) (c) Use the tabular approach to applying Bayes' theorem to compute P(A1 | B), P(A2 | B), and P(A3 | B). (Round your answers to two decimal places.) Events P(Ai) P(B | Ai) P(Ai ∩ B) P(Ai | B) A1 0.20 0.50 A2 0.30 0.30 A3 0.50 0.40 1.00 1.00The prior probabilities for events A₁, A2, and A3 are P(A₁) = 0.20, P(A₂) = 0.30, and P(A3) = 0.50. The conditional probabilities of event B given A₁, A₂, and A3 are P(B | A₁) = 0.50, P(B | A₂) = 0.30, and P(B | A3) = 0.40. (Assume that A₁, A₂, and A3 are mutually exclusive events whose union is the entire sample space.) (a) Compute P(B ʼn A₁), P(B n A₂), and P(B n A3). P(B n A₁) P(B n A₂) = P(B n A3) = P(A₁)P(B | A₁) (b) Apply Bayes' theorem, P(A¡ | B) = 7 to compute the posterior probability P(A₂ | B). (Round your answer to two decimal P(A₁)P(B | A₁) + P(A₂)P(B | A₂) + + P(An)P(B | An)' places.) (c) Use the tabular approach to applying Bayes' theorem to compute P(A₁ | B), P(A₂ | B), and P(A3 | B). (Round your answers to two decimal places.) Events P(A₁) | P(B | A;) P(A¡n B) P(A¡ | B) A₁ 0.20 0.50 A₂ 0.30 0.30 A3 0.50 0.40 1.00 1.00 0.00
- You purchase a brand new car for $15,000 and insure it. The policy pays 78% of the car's value if there is an issue with the engine or 30% of the car's value if there is an issue with the speaker system. The probability of an issue with the engine is 0.009, and the probability there is an issue with the speaker system is 0.02. The premium for the policy is p. Let X be the insurance company's net gain from this policy. (a) Create a probability distribution for X, using p to represent the premium on the policy. Enter the possible values of X in ascending order from left to right. P(X) (b) Compute the minimum amount the insurance company will charge for this policy. Round your answer to the nearest centIf events A and B are independent, then P(A U B) = 0. True or false?Please help
- Let A and B be two events with P(A and Bc) = 1. Find P(B). Recall that Bc denotes the complement of the event B.1. A and B are independent, with P (A) = 0.6, and P (B) = 0.4, calculate the following probabilities: P (A and B1) b. If A and B are independent, with P (A) = 0.6, and P (B) = 0.4, calculate the following probabilities: P (A/B) c.If A and B are independent, with P (A) = 0.6, and P (B) = 0.4, calculate the following probabilities: P (A1 and B) d.If A and B are independent, with P (A) = 0.6, and P (B) = 0.4, calculate the following probabilities: P (A or B)Let A and B be two events such that the probability of B is 0.5 and the probability of both is 0.2. Find the probability of A given that B occurs.
- John is having a dinner at a restaurant, which sells 3 kinds of dishes, A, B, and C. The probabilities of ordering each dish are 0.4, 0.3, and 0.3. Suppose the probability of John being satisfied after eating the dishes are 0.7, 0.5, and 0.6, respectively. Answer the questions below. 1) When John wasn’t satisfied with his dish, what is the probability that he has eaten the dish B? (Round an answer to two decimal places.) 2) What is the probability that John satisfies after eating the dish?Assume that we have two events A and B, that are mutually exclusive. Assume further that P(A): = 0.35 and P(B) = 0.45. Find P(A n B). Select one: O a. 0.35 О Б.0.1575 Oc. 0.65 O d. 0.45 O e. 0 O f.0.55