TEST 1 REVIEW SHEETTEST 1 REVIEW SHEETTest 1 – Friday, February 23rd1. You figure you have a 70% chance of getting an A in math, a 60% chance of getting an A in rocket science and a 10% chance you won’t get an A in either class.a. Find the probability of getting an A in either math or rocket scienceb. Find the probability of getting an A in math and rocket science.c. Given that you get an A in rocket science, what is the probability of getting an A in math?2. On a blind date, there is a 30% chance that you’ll like your date, an 80% chance that you’ll like the food and a 95% chance that you’ll like one or the other. a. Find the probability of liking your date but not the food.b. Find the probability of not liking the food nor your date.c. Are the events “liking your date” and “liking the food” independent? Why or why not? 3. Evaluate the sum: )32(732jjj4. Re-index the following summation with index j ranging from 2 to 4: 53212iii5. A department store has a box with 100 balls in it, colored green, yellow and red. A customer can enter the store and pull out a ball. If the ball is green, the customer is given $10 off a purchase of $100 or more; if the ball is yellow, the customer is given $25 off, and if the ball is red, the customer is given $50 off a purchase of $100 or more. Suppose there are 64 green balls, 26 yellow balls, and 10 red balls. a. Assuming each ball has an equal likelihood of being drawn, what is the probability of not drawing a yellow ball?b. Let X be the random variable that measures the expected discount that a customer receives. Determine XE.6. A “fair” penny is flipped 5 times in a row. a. What is the probability of obtaining 5 heads?b. Let T be the random variable that gives the number of tails obtained in 5 flips. Find )1( TP and 1TP7. You have the following data: 20% of Acer computers malfunction within the first year,15% of Gateways and 12% of Dell computers malfunction within the first year. Yourcompany just purchased 50 Acers, 40 Gateways and 37 Dells.a. What is the probability that a computer you have just purchased willmalfunction within the first year? b. A computer malfunctions. What is the probability that it is a Dell?8. A rash of a serious mental condition called Sparticacitus is sweeping our nation,affecting 40% of the population. There is a test of Sparticacitus; it gives false positives2% of the time, and false negatives 4% of the time.Note: A false positive means you don’t have Sparticacitus, but the test says you do. A false negative means you do have Sparticacitus, but the test says you don’t. a. You don’t know if you have Sparticacitus. You get tested; what is theprobability that you’ll test positive?b. The test says that you have Sparticacitus. What is the probability that you truly have it?c. You do not have Sparticacitus. What is the probability that the test will say that you have it?9. In a certain small town, 16% of the population developed lung cancer. If 45% ofthe population are smokers, and 85% of those developing lung cancer are smokers, whatis the probability that a smoker in this population will develop lung cancer? 10. Using a Venn diagram, sketch the following sets:a. CCBA )(b. CBAC
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