Econ_120A_week_4_Soln.pdf - Econ 120A Week 4 Worksheet Solutions Sabareesh Ramachandran You may not yourself or allow others to reproduce or distribute

Econ_120A_week_4_Soln.pdf - Econ 120A Week 4 Worksheet...

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Econ 120A: Week 4 Worksheet Solutions Sabareesh Ramachandran October 22, 2019 You may not yourself or allow others to reproduce or distribute lecture notes and course materials publicly whether or not a fee is charged without my express written consent. Doing so will be in violation of the University Code of Student Conduct, Part 9(k). Questions are in black. Solutions are in blue. 1. (SP13) Forbes collects and records annually information on the 40 best-paid CEO’s. Besides salary information, Forbes collects information on the level of education. The following table gives the data on the highest degree obtained by those 40 best-paid CEO’s in 2011: Degree Number of CEOs Bachelors 13 Law 1 Masters 5 MBA 15 None 4 PhD 2 Total 40 (a) What is the probability that the highest degree of a randomly selected CEO is a Ph.D. degree? Show your work. (b) You select two CEOs at random (without replacement) and record the highest degree obtained by each. What is the probability of selecting one CEO whose highest degree is a Masters and one CEO whose highest degree is a MBA? Show your work. (c) You select two CEOs at random (without replacement) and record the highest degree obtained by each. What is the probability that at least one CEO has an advanced degree? Note: Advanced degrees are Masters, MBA, Law and Ph.D. Show your work. (d) You select five CEOs at random (without replacement) and record the highest degree obtained by each. Suppose the highest degree obtained by each of the first four CEOs you selected is a bachelor’s degree. What is the probability that the highest degree obtained by the fifth CEO you select is a bachelor’s degree? Show your work. Solution : (a) Pr ( PhD ) = NumberofPhD Total = 2 40 = 0.05 (b) Let us denote the event that the first person you select has a Masters degree as Masters 1 , the event that the second person you select has a masters degree as Masters 2 , the first person you select has a MBA degree as MBA 1 and the second person you select has a MBA degree as MBA 2 . From above we know that, Pr ( Masters 1 ) = 0 . 125 and Pr ( MBA 1 ) = 0 . 375. Now, the event described in the question can happen if the first person has a Masters degree and the second person has a MBA degree ( Masters 1 and MBA 2 ) or if the first person has a MBA degree and the second person has a masters degree ( MBA 1 and Masters 2 ). Hence we need to find the probability Pr (( Masters 1 and MBA 2 ) or ( MBA 1 and Masters 2 )). Since the two events are mutually exclusive, this is equal to Pr ( Masters 1
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