Statistic and probability
Classifying Events In Exercises 58, decide whether the events are independent or dependent. Explain your reasoning. 5. Selecting a king from a standard deck, replacing it, and then selecting a queen from the deck 6. Parking beside a re hydrant on Tuesday and getting a parking ticket on Tuesday 7. A numbered ball between 1 and 40 is selected from a bin, and then a second numbered ball is selected from the remaining balls in the bin. 8. A numbered ball between 1 and 52 is selected from a bin, replaced, and then a second numbered ball is selected from the bin. 9. BRCA Gene 6 In the general pepulation, one woman in nine will develop breast cancer. Research has shown that one woman in 250 carries a mutation of the BRCA gene Eight out of 10 women with this mutation develop breast cancer. (Source: Journal of National Cancer Institute) (3) Find the probability that a randomly selected woman will deveIOp breast cancer, given that she has a mutation of the BRCA gene. (b) Find the probability that a randomly selected woman will carry the mutation of the BRCA gene and will develop breast cancer. (0) Are the events of carrying this mutation and developing breast cancer independent or dependent? Explain. ' Breast Cancer and the BRCA Gene Women who develop breast ' ' this year independent or dependent events? Explain. 11. Assisted Reproductive Technology 0 A Pregnancies study found that 24% of the assisted repro- __ ductive technology (ART) cycles resulted in a pregnancy. Seven percent of the ART pregnancies resulted in multiple births. (Source: U.S. Department of Health and Human Services} '. a (a) Find the probability that a randomly selected ART cycle resulted in a5, pregnancy and produced a multiple birth. is (b) Find the probability that a randomly selected ART cycle that resulted in a pregnancy did not produce a multiple birth. iii Race Relations 12. Race Relations 9 In a survey, 60% of adults in the U.S. think race relations have improved since the death of Martin Luther King, In or these 60%, 4 out of 10 said the rate of civil rights progress is too slow. (Source: Maris: Institute for Pnbh'c Opinion) (a) Find the probability that a randomly selected adult thinks race relations have improved since the death of Martin Luther King, Jr. and thinks the "xrate of civil rights progress is too slow. (b) Given that a randomly selected adult. thinks race relations ha": improved since the death of Martin Luther King, In, find the probab'jlt that he or she thinks the rate of civil rights progress is not too slow. '- 13. Defective Ports 9 In a box of 11 parts, four of the parts are defective. ' parts are selected at random without replacement. I (a) Find the probability that both parts are defective. (b) Find the prob ability that both parts are not defective. (c) Find the probability that at least one part is defective. SECTION 3.2 Conditional Probability and the Multiplication Rule 127 14. Light Bulbs 9 Twelve light bulbs are tested to see if they last as long as the manufacturer claims they do. Three light bulbs fail the test. Two light bulbs are selected at tandem without replacement. (a) Find the probability that both light bulbs failed the test. (b) Find the probability that both light bulbs passed the test. (c) Find the probability that at least one light bulb failed the test. 15. Emergency Savings 9 The following table shows the results of a survey in which 102 men and 103 women workers ages 25 to 64 were asked if they have at least one month's income set aside fer emergencies. (Adapted from. Merrill Lynch.) 9
