MATH 411 Final Exam-Fa1l 2017 Score: 75 Name Write al the details and commands u
ID: 3322511 • Letter: M
Question
MATH 411 Final Exam-Fa1l 2017 Score: 75 Name Write al the details and commands used. Simplify all answers to 4 decimals. 1) An urn has 6 red and 12 blue balls. You draw balls one at a time and with replacement. Seati (5 points) a) What is the probability that the 8-th ball drawn is the 6-th blue ball. b) If y is the number of draws to get the 6-th blue ball, what is the expected value of Y 2) A population of voters have 60% Males,40% Females. It is reported that 60% of the Males favors proposal A while 30% of the Females favor proposal A . If you select a person at random, find: a) The probability he favors proposal A. 6 points) b) The probability bhe is a male given that he favors proposalA.Explanation / Answer
1)Give that urn contains 6 red and 12 blue balls
No of ways of chosing r balls from n balls = nCr = n!/(r!*(n-r)!)
a)
Given that balls are drawn with replacement
Probability of red ball = 6/(6+12) = 1/3
Probability of blue ball = 12/(6+12) = 2/3
Probability that 8 th ball drawn is 6th blue ball = Probability that 5 out of first 7 balls are blue *Probability that 8 th ball drawn is blue
= (7C5)(2/3)5(1/3)2 * (2/3)
= 0.2048
b)
we know that
Probability of getting a first blue ball follows the geometric distribution with p=2/3
Expected . no of draws for getting first blue ball = 1/p = 1/(2/3) = 3/2 = 1.5
Expected . no of draws for getting 6th blue ball = 6*Expected . no of draws for getting a blue ball
= 6*1.5 = 9
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