1. A box of nine gloves contains two left-handed gloves and seven right-handed gloves. (a) If two gloves are randomly selected from the box, without replacement (the first glove is not returned to the box after it is selected), what is the probability that both gloves selected will be right-handed? 7 6 42 ool 72 (b) If two gloves are randomly selected from the box, without replacement (the first glove is not returned to the box after it is selected), what is the probability that there will be one right-handed glove and one left-handed glove selected? 2 7 7 7 3 78 (c) If three gloves are selected, with replacement, what is the probability that all three will be Left-handed? 8 729 (d) If you were sampling with replacement, what would be the answers to (a) and (b)? a: O' =. b: _ _= - 14 2. Olive Construction Company is determining whether it should submit a bid for a new shopping center. In the past, Olive's main competitor, Base Construction Company, has submitted bids 70% of the time. If Base Construction Company does not bid on a job, the probability that Olive- Construction Company will get the job is 0.50. If Base Construction Company bids on a job, the probability that Olive Construction Company will get the job is 0.25. (a) If Olive Construction Company gets the job, what is the probability that Base Construction Company did not bid? P(A)=(0.25.0.70)+(0.50-0.30) P(B|A)= 0.5*0.3 - = 0.4615 P(A) (b) What is the probability that Olive Construction Company will get the job? P(A) = (0.25x0.70) + (0.50x0.30) = 0.175+0.15 = 0.325 3. A student is taking a multiple-choice exam in which each question has four choices. Assume that the student has no knowledge of the correct answers to any of the questions. She has decided on a strategy in which she will place four balls (marked A, B, C, and D) into a box. She randomly selects one ball for each question and replaces the ball in the box. The marking on the ball will determine her answer to the question. There are five multiple choice questions on the exam. What is the probability that she will get (a) Five questions correct? (b) At least four questions correct? (c) No questions correct? (d) No more than two questions correct? Using the binomial probability formula, p = 14, (1-p) = 3/4 a: n = 5, probability = 0.098% b: n = 4_probability = 1.56% c: n = 0_probability = 23.73% d: n =2_probability = 89.65%