SECTION 3.2 Conditional Probability and the Multiplication Rule 153 Classifying Events as Independent or Dependent In Exercises 9–14, determine whether the events are independent or dependent. Explain your reasoning. 9. Selecting a king from a standard deck of 52 playing cards, replacing it, and then selecting a queen from the deck 10. A father having hazel eyes and a daughter having hazel eyes 11. Returning a rented movie after the due date and receiving a late fee 12. Not putting money in a parking meter and getting a parking ticket 13. Rolling a six-sided die and then rolling the die a second time so that the sum of the two rolls is five 14. A ball is selected from a bin of balls numbered from 1 through 52. It is replaced, and then a second numbered ball is selected from the bin. Classifying Events Based on Studies In Exercises 15–18, identify the two events described in the study. Do the results indicate that the events are independent or dependent? Explain your reasoning. 15. A study was conducted to debunk the idea that abilities in music and math are related. Instead, the study showed a strong relationship between achievements in music and math. (Source: University of Kansas) 16. A study found no significant association between the use of talc powder and the incidence of ovarian cancer in women. (Source: JAMA) 17. A study found that there is no relationship between playing violent video games and aggressive or bullying behavior in teenagers. (Source: The Royal Society Publishing) 18. A study found that business executives with high levels of self-leadership traits are more likely to attribute successes to their own efforts. (Source: Pollack Peacebuilding Systems) Using the Multiplication Rule In Exercises 19–32, use the Multiplication Rule. 19. Cards Two cards are selected from a standard deck of 52 playing cards. The first card is not replaced before the second card is selected. Find the probability of selecting a heart and then selecting a club. 20. Coin and Die A coin is tossed and a die is rolled. Find the probability of tossing a tail and then rolling a number greater than 2. 21. BRCA1 Gene Research has shown that approximately 1 woman in 400 carries a mutation of the BRCA1 gene. About 64% of women with this mutation develop breast cancer. Find the probability that a randomly selected woman will carry the mutation of the BRCA1 gene and will develop breast cancer. (Source: National Cancer Institute) Sample Space: Women Women with mutated BRCA1 gene Women who develop breast cancer
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