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2. Given events A, B, and C such that P(A) = .3, P(B) = .2, and P(C) = .5. Events A and B are independent. Compute P(An B|C).

2. Given events A, B, and C such that P(A) = .3, P(B) = .2, and P(C) = .5. Events A and B are independent. Compute P(An B|C).

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Expert Q&A** Answer the following questions and show all the steps: 2. Given events A, B, and C such that P(A) = 0.3, P(B) = 0.2, and P(C) = 0.5. Events A and B are independent. Compute P(A ∩ B|C). 3. Suppose the probability that a six-sided die will land on an odd number is 0.45. If we roll the die seven times, what is the probability that we will get less than four odd numbers? Assume die rolls are independent. 4. If the probability of a success in a chance experiment is 0.32, and we continue to perform trials of the experiment until our first success, what is the probability that the chance experiment will run for more than three trials? Assume all trials are independent. 5. Compute the following probabilities for the following normal distributions: (a) μ=1, σ=0.5 find P(0.7 < x < 1.2). (b) μ=15, σ=2 find P(13 < x). (c) μ=100, σ=12 find P(x < 97 or x > 106). 6. Given the following probabilities from a normal distribution with random variable x corresponding to μ = 4 and σ = 0.8 then compute the following x* value. (a) P(z < z*) = 0.9861 (b) P(z > z*) = 0.8264 (c) P(z < -z* or z > z*) = 0.25 7. What is a sufficient sample size for constructing a 90% confidence interval with margin of error, M equal to 3%? 8. Construct a 95% confidence interval for the population mean given sample mean x̄ = 7.5, sample standard deviation s = 0.49, and sample size n = 9.
Transcribed Image Text:**Expert Q&A** Answer the following questions and show all the steps: 2. Given events A, B, and C such that P(A) = 0.3, P(B) = 0.2, and P(C) = 0.5. Events A and B are independent. Compute P(A ∩ B|C). 3. Suppose the probability that a six-sided die will land on an odd number is 0.45. If we roll the die seven times, what is the probability that we will get less than four odd numbers? Assume die rolls are independent. 4. If the probability of a success in a chance experiment is 0.32, and we continue to perform trials of the experiment until our first success, what is the probability that the chance experiment will run for more than three trials? Assume all trials are independent. 5. Compute the following probabilities for the following normal distributions: (a) μ=1, σ=0.5 find P(0.7 < x < 1.2). (b) μ=15, σ=2 find P(13 < x). (c) μ=100, σ=12 find P(x < 97 or x > 106). 6. Given the following probabilities from a normal distribution with random variable x corresponding to μ = 4 and σ = 0.8 then compute the following x* value. (a) P(z < z*) = 0.9861 (b) P(z > z*) = 0.8264 (c) P(z < -z* or z > z*) = 0.25 7. What is a sufficient sample size for constructing a 90% confidence interval with margin of error, M equal to 3%? 8. Construct a 95% confidence interval for the population mean given sample mean x̄ = 7.5, sample standard deviation s = 0.49, and sample size n = 9.
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