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ec41f10_hw2_sol

ec41f10_hw2_sol - Kata Bognar [email protected] Economics 41...

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Kata Bognar [email protected] Economics 41 Statistics for Economists UCLA Fall 2010 Homework Assignment 2. - suggested solutions by Gonca Senel - Conditional Probability. 1. A fair coin is flipped twice. Let the events A = “the first toss is heads” , B = “the second toss is heads” and C = “at least one toss is heads” . Determine the following probabilities. Answer: The outcome space for this random experiment is { HH, HT, TH, TT } . A = { HH, HT } B = { HH, TH } C = { HH, HT, TH } A B = { HH } B C = { HH, TH } A C = { HH, HT } C B 0 = { HT } . Each outcome is equally likely therefore, (a) P ( B ) = 1 2 (b) P ( B | A ) = 1 / 4 2 / 4 = 1 2 (c) P ( B | C ) = 2 / 4 3 / 4 = 2 3 (d) P ( C ) = 3 4 (e) P ( C | A ) = 2 / 4 2 / 4 = 1 (f) P ( C | B 0 ) = 1 / 4 2 / 4 = 1 2 2. Two independent events are: (a) always mutually exclusive events (b) never mutually exclusive events (c) always complementary events (d) always subjective events 3. An independent research team inspects 500 batteries manufactured by two companies for being good or defective. The following table gives the two-way classification of these 500 batteries. Good Defective Company A 150 50 Company B 260 40 (a) The team selects one battery randomly from these 500 batteries. Find the probability that this battery: Answer: Define the following events: A = “the battery selected is manufactured by company A” , B = “the battery selected is manufactured by company B” , G = “the battery selected is good” and D = “the battery selected is defective” . 1

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i. is manufactured by company B: Answer: P ( B ) = 300 500 ii. is defective: Answer: P ( D ) = 90 500 iii. is good given that it is manufactured by company B: Answer: P ( G | B ) = 260 300 iv. is manufactured by company A given that it is defective: Answer: P ( A | D ) = 50 90 .
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