Is Event B dependent or independent of Event A? 7) 7) A: A green ball is drawn from a box with five balls and placed next to the box. B: A red ball is drawn next and placed next to the green one. A) Dependent B) Independent Find the indicated probability. 8) In one town, \( 44 \% \) of all voters are Democrats. If two voters are randomly selected for a survey, find the probability that they are both Democrats. Round to the nearest thousandth if necessary, A) 0.440 B) 0.880 C) 0.189 D) 0.194 9) Find the probability of correctly answering the first 2 questions on a multiple choice test if random guesses are made and each question has 3 possible answers. A) \( \frac{3}{2} \) B) \( \frac{1}{8} \) C) \( \frac{2}{3} \) D) \( \frac{1}{9} \) 9) 10) A batch consists of 12 defective coils and 88 good ones. Find the probability of getting two good coils when two coils are randomly selected if the first selection is replaced before the second is made. A) 0.176 B) 0.7733 C) 0.7744 D) 0.0144 11) A bin contains 67 light bulbs of which 11 are defective. If 4 light bulbs are randomly selected from 11) the bin with replacement, find the probability that all the bulbs selected are good ones. Round to the nearest thousandth if necessary. A) 0.836 B) 0.001 C) 0.488 D) 0.544 12) In one town, \( 77 \% \) of adults have health insurance. What is the probability that 10 adults selected at random from the town all have health insurance? Round to the nearest thousandth if necessary. A) 7.7 B) 0.13 C) 0.073 D) 0.77 13) A study conducted at a certain college shows that \( 58 \% \) of the school's graduates find a job in their chosen field within a year after graduation. Find the probability that 10 randomly selected graduates all find jobs in their chosen field within a year of graduating. Round to the nearest thousandth if necessary. A) 0.007 B) 0.004 C) 5.800 D) 0.172 14) You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing 14) cards. Find the probability that both cards are black. Express your answer as a simplified fraction. A) \( \frac{25}{51} \) B) \( \frac{1}{2,652} \) C) \( \frac{25}{102} \) D) \( \frac{13}{51} \)

Below are the step‐by‐step explanations and answers for each problem: ───────────────────────────── 1) Problem 7 ───────────────────────────── Event A: A green ball is drawn from a box with five balls and then placed aside (i.e. it is not returned). Event B: A red ball is drawn next from the box. Because the green ball is not replaced, the composition of the balls in the box changes. That means the outcome of Event A affects the probabilities for Event B. Therefore, Event B is dependent on Event A. Answer for 7: A) Dependent ───────────────────────────── 2) Problem 8 ───────────────────────────── In one town, 44% of the voters are Democrats. When two voters are randomly selected, the probability that both are Democrats is computed by multiplying the individual probability (assuming independence for such a survey): Probability = 0.44 × 0.44 = 0.1936 Rounded to the nearest thousandth, this is 0.194. Answer for 8: D) 0.194 ───────────────────────────── 3) Problem 9 ───────────────────────────── On a multiple‐choice test each question has 3 possible answers. If you guess at random, the probability of getting one question correct is 1/3. For the first 2 questions both to be answered correctly: Probability = (1/3) × (1/3) = 1/9 Answer for 9: D) 1/9 ───────────────────────────── 4) Problem 10 ───────────────────────────── A batch of coils consists of 12 defective and 88 good coils (total 100). When two coils are selected with replacement, the probability that a single coil selected is good is 88/100 = 0.88. Since the selection is made with replacement, the draws are independent: Probability = 0.88 × 0.88 = 0.7744 Answer for 10: C) 0.7744 ───────────────────────────── 5) Problem 11 ───────────────────────────── A bin contains 67 light bulbs, 11 of which are defective. Therefore, the number of good bulbs is 67 – 11 = 56. Four bulbs are selected with replacement. The probability that one bulb selected is good is 56/67. Thus, the probability that all four are good is: Probability = (56/67)⁴ Calculate (56/67) approximately: 56/67 ≈ 0.8358 Then, (0.8358)⁴ ≈ 0.488 (rounded to the nearest thousandth) Answer for 11: C) 0.488 ───────────────────────────── 6) Problem 12 ───────────────────────────── In a town, 77% (0.77) of adults have health insurance. For 10 randomly selected adults, the probability that they all have health insurance is: Probability = 0.77¹⁰ Calculating 0.77¹⁰ gives approximately 0.073 (when rounded to the nearest thousandth). Answer for 12: C) 0.073 ───────────────────────────── 7) Problem 13 ───────────────────────────── A study shows that 58% (0.58) of graduates find a job in their chosen field within a year. For 10 randomly selected graduates, the probability that they all secure jobs in their chosen field is: Probability = 0.58¹⁰ Calculating 0.58¹⁰, you get approximately 0.004 (rounded to the nearest thousandth). Answer for 13: B) 0.004 ───────────────────────────── 8) Problem 14 ───────────────────────────── You are dealt two cards successively without replacement from a standard 52‐card deck. The probability that the first card is black is 26/52 = 1/2. After drawing one black card, there are 25 black cards left in a deck of 51 cards. Thus, the probability that the second card is black is 25/51. Multiply the two probabilities: Probability = (26/52) × (25/51) = 1/2 × 25/51 = 25/102 Answer for 14: C) 25/102 ───────────────────────────── Summary of Answers ───────────────────────────── 7) A) Dependent 8) D) 0.194 9) D) 1/9 10) C) 0.7744 11) C) 0.488 12) C) 0.073 13) B) 0.004 14) C) 25/102