Female

130

90

a. Select one student randomly from this group of 400 students. What is the probability that this student: (i) does not work (ii) is a female (iii) does not work given he is a male (iv) is a female given she works b. Are the events “male” and “do not work” mutually exclusive? Explain why or why not. c. Are the events “female” and “do not work” independent? Explain why or why not. d. What is the complementary event of the event “do not work”? What is the probability of this complementary event? 10. An independent research team inspects 300 batteries manufactured by two companies for being good or defective. The following table gives the two-way classification of these 300 batteries. Company A Company B

Good 140 130

Defective 10 20

a. The team selects one battery randomly from these 300 batteries. Find the probability that this battery: (i) is manufactured by company B (ii) is defective (iii) is good given that it is manufactured by company B (iv) is manufactured by company A given that it is defective b. Are the events “company A” and “defective” mutually exclusive? Explain why or why not. c. Are the events “good” and “company A” independent? Explain why or why not. d. What is the complementary event of the event “defective”? What is the probability of this complementary event?

11. There are a total of 300 professors at a university. Of them, 75 are female and 90 are professors in the social sciences. Of the 75 females, 30 are professors in social sciences. Are the events “female” and “professor in social sciences” independent? Are they mutually exclusive? Explain why or why not? 12. There are a total of 40 students in a class. Of them, 18 are male and 14 are seniors. Of the 18 males, six are seniors. Are the events “male” and “senior” independent? Are they mutually exclusive? Explain why or why not. 13. Let A be the event that a randomly selected family owns a house. The probability of event A is .68. What is the complementary event of A, and what is its probability? 14. Let A be the event that a randomly selected employee of a company is in favor of labor unions. The probability of event A is .56. What is the complementary event of A, and what is its probability? 15. The following table gives a two-way classification of all employees of a company based on their sex and whether or not they are college graduates.

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