Suppose A and B are events in a sample space with:\[ P(A) = 0.6, \, P(B) = 0.65, \, P(B \cup A) = 0.84 \]Find the following probabilities.\[ P(A \cap B) = 0.41 \]\[ P(B|A) = \, \_\_\_\_ \]\[ P(A|B) = \, \_\_\_\_ \]This image provides information regarding the probabilities of two events, A and B. It specifies the individual probabilities of A and B, the probability of either A or B occurring (union), and the probability of both A and B occurring together (intersection).The conditional probabilities \( P(B|A) \) and \( P(A|B) \) are left to be determined.

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Answered: Suppose A and B are events in a sample…

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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D An oil company purchased an option on land in Alaska. Preliminary geologic studies assigned the following prior probabilities. P(high-quality oil) = 0.40 P(medium-quality oil) = 0.25 P(no oil) = 0.35 a. What is the probability of finding oil (to 2 decimals)? b. After 200 feet of drilling on the first well, a soil test is taken. The probabilities of finding the particular type of soil identified by the test are given below. P(soil|high-quality oil) = 0.25 P(soil|medium-quality oil) = 0.90 P(soil|no oil) = 0.25 %3D Given the soil found in the test, use Bayes' theorem to compute the following revised probabilities (to 4 decimals). P(high-quality oil|soil) P(medium-quality oil soil) P(no oil soil) What is the new probability of finding oil (to 4 decimals)? According to the revised probabilities, what is the quality of oil that is most likely to be found? - Select your answer -
An experiment consists of two independent trials. The outcomes of the first trial are A, B, and C, with probabilities of occurring equal to 0.2, 0.4, and 0.4, respectively. The outcomes of the second trial are E and F, with probabilities of occurring equal to 0.7 and 0.3. Draw a tree diagram representing this experiment. Use this tree diagram to find the probabilities below. (a) P(B)(b) P(F | B)(c) P(B F)(d) P(F)(e) Does P(B F) = P(B) · P(F)? YesNo (f) Are B and F independent events? YesNo
A restaurant owner wanted to know which time range are popular among the customers. Data were collected on the following events: L = a customer usually visits the restaurant during lunch time D = a customer usually visits the restaurant during dinner time Data collected suggest the following: P( L ) = 0.6 P( D ) = 0.7 P( L and D) = 0.3 What is the possibility that a customer only visit the restaurant during dinner time
An oil company purchased an option on land in Alaska. Preliminary geologic studies assigned the following prior probabilities. P(high-quality oil) = 0.45 P(medium-quality oil) = 0.25 P(no oil) = 0.30 a. What is the probability of finding oil (to 2 decimals)? 0.70 b. After 200 feet of drilling on the first well, a soil test is taken. The probabilities of finding the particular type of soil identified by the test are given below. P(soil high-quality oil) = 0.20 P(soil medium-quality oil) = 0.90 P(soil no oil) 0.20 Given the soil found in the test, use Bayes' theorem to compute the following revised probabilities (to 4 decimals). P(high-quality oil soil) 0.2308 P(medium-quality oil soil) 0.5769 X P(no oil soil) 0.1538 What is the new probability of finding oil (to 4 decimals)? Medium-quality 0.8077 According to the revised probabilities, what is the quality of oil that is most likely to be found?
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If A and B are independent events, P(A)=0.28, and P(B)=0.67, what is P(B|A)?

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Suppose A and B are events in a sample space with P(A) = 0.6, P(B) = 0.65, P(BUA) = 0.84 Find the following probabilities. P(An B) = 0.41 P(B|A) = P(A|B) =