P(A)=0.56,P(B)=0.52,P(B∩A¯¯¯¯)=0.32P(A)=0.56,P(B)=0.52,P(B∩A¯)=0.32 Find the following probabilities. P(A)P(A) = P(A∪B)P(A∪B) = P(A∪B¯¯¯¯¯¯¯¯¯¯¯¯¯)P(A∪B¯) = P(A∩B)P(A∩B) = P(A¯¯¯¯)P(A¯) = P(A∩B¯¯¯¯¯¯¯¯¯¯¯¯¯)P(A∩B¯) = P(A¯¯¯¯∪B)P(A¯∪B) =

P(A)=0.56,P(B)=0.52,P(B∩A¯¯¯¯)=0.32P(A)=0.56,P(B)=0.52,P(B∩A¯)=0.32 Find the following probabilities. P(A)P(A) = P(A∪B)P(A∪B) = P(A∪B¯¯¯¯¯¯¯¯¯¯¯¯¯)P(A∪B¯) = P(A∩B)P(A∩B) = P(A¯¯¯¯)P(A¯) = P(A∩B¯¯¯¯¯¯¯¯¯¯¯¯¯)P(A∩B¯) = P(A¯¯¯¯∪B)P(A¯∪B) =

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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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 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
Choose the correct option. (a)−3 (b)3 (c)-5 (d)5
Suppose we know that the probabilities P(A) = .5, P(B|A) = .3 and P(A or B) =.3. What is the value for P(A and B)? What is the value for P(B)?
Suppose that Trendy Inc. products a style of a seasonal business suit, Sit-T-Slicker, which has a cost of $500 per unit. The demand during the season for Sit-T-Slicker is generally unknown and could be either: 200, 500, 800, 1100, and 1500 units with equal probabilities. Trendy sells the Sit-T-Slicker suit for $900 per unit during its three-month season, and for $300 per unit when sold after that time. Given the above data, what is the optimal order quantity for the Sit-T-Slicker? What is expected profit? Suppose the probabilities in part a change to 0.05, 0.25, 0.40, 0.25, 0.05 for demand levels 200, 500, 800, 1100, 1500, respectively. What is the optimal order quantity and expected profit in this case? How would better information regarding the demand for the Sit-T-Slicker suit change the data provided in this problem? How would this information affect the answers to part a? Explain.
(QUEEN'S SECRET AND GENIES) In old days, there was a queen and she had a secret problem to solve. To get an answer to her secret problem, the queen bought one female and one male genie lamps. The probabilities that her secret problem can be solved by the male and female genies are 0.3 and 0.4 respectively. A Queen looking for divine help. Assume the queen keeps the genies independently away from each other with a fear that both could not harm her, what is the probability that the queen's secret problem is solved by at least one of the genies? Note: Please keep accuracy upto two decimal places.
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Javier volunteers in community events each month. He does not do more than five events in a month. He attends exactly five events 30% of the time, four events 25% of the time, three events 25% of the time, two events 10% of the time, one event 5% of the time, and no events 5% of the time.(a) Find the probability that Javier volunteers for less than three events each month. P(X < 3) = (b) Find the expected number of events Javier volunteers in a month. dont round
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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)