1. A set of ten cards consists of five red cards and five black cards. The cards are shuffled thoroughly and I am given the first four cards. I count the number of red cards X in these four cards. The random variable X has which of the following probability distributions?
A. the binomial distribution with parameters n = 10 and p = 0.5.
B. the binomial distribution with parameters n = 4 and p = 0.5.
C. Neither choice is correct.
2. A high school has 1000 students. As a school project, the school conducts a mock lottery. Each student in the school is asked to select an integer between 1 and 1000, independently of the choices of the other students. Each student gives their selection, with their name, to the school principal. The school principal uses a random number generator to select an integer between 1 and 1000 and any student that picked this number is declared a winner. What is the probability that no student wins?
A. 0. There are 1000 students and 1000 numbers, so some student must win.
B. (0.999)1000
C. 0.1587
3. There are twenty multiple-choice questions on an exam, each having responses a, b, c, or d. Each question is worth 5 points and only one response per question is correct. Suppose a student guesses the answer to each question, and her guesses from question to question are independent. If the student needs at least 40 points to pass the test, the probability the student passes is closest to
A. 0.0609.
B. 0.1019.
C. 0.9590.