Mathematics 381: Binomial Distribution and Negative Binomial Distribution Practice. 1. Suppose that 5% of the items produced by a factory are defective. If 8 items are chosen at random, what is the probability that: (a) exactly 1 is defective (b) exactly 2 are defective (c) at least 1 is defective (d) less than 3 are defective 2. Assume the probability that births of boys and girls are equally likely. In a family of 6 kids (a) what is the probability that there are 3 boys and 3 girls? (b) What is the probability of exactly 4 girls? (c) What is the probability of at least 2 boys? 3. A baseball player has a .250 batting average. What is the probability that this player will: (a) get exactly 2 hits in 4 at bats? (b) get more than 4 hits in 9 at bats? (c) get at least 2 hits in 5 at bats? 4. Consider a 20 question multiple choice test where each question has 5 choices. (a) A student guesses randomly on each question. What is the chance that this student will answer more than half the questions correctly? What is the chance that this student will answer more than 14 questions correctly? (b) Another student is able to eliminate 2 incorrect answers for each of the questions. She guesses randomly from the remaining 3 questions. What is the chance that she will answer more than half the questions correctly? What is the chance that she will answer more than 14 questions correctly? 5. What is the probability that a fair coin must be tossed exactly 10 times to observe exactly 3 heads? 6. Using the information in problem #1, what is the probability that exactly 25 items will be chosen randomly to observe the first defective item