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All answers should be in radians not degrees. 1) (15 pts total) Conditional Probability Two integrated circuits made from the same wafer are tested. Each IC either passes the test or fails the test. The event that the first IC fails the test is called A. The event that the second IC fails the test is called B. The probability of A, P(A)=0.02. The probability of B, P(B)=0.02. The probability that both ICs fail is ?(?∩?)?? 0.01. What is the conditional probability P(B|A) the the 2nd IC fails the test given that the first IC failed the test? 2) (20 points total) Sampling with replacement The NAU student ID number is a 7-digit number. Assume all numbers are randomly generated, and all numbers are equally likely to be generated. a) (5 ???) How many possible student ID numbers are there? b) (5 ???) What is the probability of getting the ID number that is all 1s, 1111111? c) (5 ???) How many student ID numbers have a 1 as the first digit? d) (5 ???) What is the probability of getting a student ID number with a 1 as the first digit? 3) (15 pts total) Sampling without replacement A box in the EE188 lab contains 200 resistors that are labeled 100kΩ resistors. Five of these resistors are in fact 10 kΩ resistors (only 5!) Your circuit design uses 3 100 kΩ resistors. a) (5 pts) What is the probability that all 3 of the resistors you choose are 100kΩ resistors? b) (5 pts) What is the probability that one or more or the 3 resistors that you chose aren’t 100 kΩ resistors? Hint: use the answer from part a) c) (5 pts) What is the probability that all 3 resistors that you chose are not 100 kΩ resistors. 4) (20 pts total) Combinations: Arrangements where order doesn’t matter a) (3 pts) How many ways are there to draw 3 resistors from a box of 200 resistors? b) (3 pts) How many ways are there to draw 3 resistors from a group of 195 100 kΩ resistors? c) (4 pts) Calculate the probability of drawing 3 100 kΩ resistors from a box of 200 resistors, where 195 are 100 kΩ resistors and 5 are 10 kΩ resistors. Use your results from a) and b) to find this probability. d) (2 pts) Is your answer in c) the same as 3a)? e) (3 pts) How many ways are there to draw 3 resistors from a group of 5 10 kΩ resistors? f) (3 pts) Calculate the probability of drawing 3 10 kΩ resistors from a box of 200 resistors, where 195 are 100 kΩ resistors and 5 are 10 kΩ resistors. Use your results from a) and e) to find this probability. g) (2 pts) Is your answer in f) the same as your answer from 3c)? 5) (20 pts) For the following data set: 70.6, 70.9, 69.1, 71.3, 70.5, 69.7, 71.5, 69.8, 71.1, 68.9, 70.3, 69.2, 71.2, 70.4, 72.8 a) (5 pts) Draw a histogram with bin size 0.5, starting at the bin 68.45-68.95 b) (5 pts) What is the mean of the data? c) (5 pts) What is the median of the data? d) (5 pts) What is the standard deviation of the data?

## All answers should be in radians not degrees. 1) (15 pts total) Conditional Probability Two integrated circuits made from the same wafer are tested. Each IC either passes the test or fails the test. The event that the first IC fails the test is called A. The event that the second IC fails the test is called B. The probability of A, P(A)=0.02. The probability of B, P(B)=0.02. The probability that both ICs fail is ?(?∩?)?? 0.01. What is the conditional probability P(B|A) the the 2nd IC fails the test given that the first IC failed the test? 2) (20 points total) Sampling with replacement The NAU student ID number is a 7-digit number. Assume all numbers are randomly generated, and all numbers are equally likely to be generated. a) (5 ???) How many possible student ID numbers are there? b) (5 ???) What is the probability of getting the ID number that is all 1s, 1111111? c) (5 ???) How many student ID numbers have a 1 as the first digit? d) (5 ???) What is the probability of getting a student ID number with a 1 as the first digit? 3) (15 pts total) Sampling without replacement A box in the EE188 lab contains 200 resistors that are labeled 100kΩ resistors. Five of these resistors are in fact 10 kΩ resistors (only 5!) Your circuit design uses 3 100 kΩ resistors. a) (5 pts) What is the probability that all 3 of the resistors you choose are 100kΩ resistors? b) (5 pts) What is the probability that one or more or the 3 resistors that you chose aren’t 100 kΩ resistors? Hint: use the answer from part a) c) (5 pts) What is the probability that all 3 resistors that you chose are not 100 kΩ resistors. 4) (20 pts total) Combinations: Arrangements where order doesn’t matter a) (3 pts) How many ways are there to draw 3 resistors from a box of 200 resistors? b) (3 pts) How many ways are there to draw 3 resistors from a group of 195 100 kΩ resistors? c) (4 pts) Calculate the probability of drawing 3 100 kΩ resistors from a box of 200 resistors, where 195 are 100 kΩ resistors and 5 are 10 kΩ resistors. Use your results from a) and b) to find this probability. d) (2 pts) Is your answer in c) the same as 3a)? e) (3 pts) How many ways are there to draw 3 resistors from a group of 5 10 kΩ resistors? f) (3 pts) Calculate the probability of drawing 3 10 kΩ resistors from a box of 200 resistors, where 195 are 100 kΩ resistors and 5 are 10 kΩ resistors. Use your results from a) and e) to find this probability. g) (2 pts) Is your answer in f) the same as your answer from 3c)? 5) (20 pts) For the following data set: 70.6, 70.9, 69.1, 71.3, 70.5, 69.7, 71.5, 69.8, 71.1, 68.9, 70.3, 69.2, 71.2, 70.4, 72.8 a) (5 pts) Draw a histogram with bin size 0.5, starting at the bin 68.45-68.95 b) (5 pts) What is the mean of the data? c) (5 pts) What is the median of the data? d) (5 pts) What is the standard deviation of the data?

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