1. A quiz has 5 multiple-choice questions where each question has 4 possible answers but only 1 is the correct answer.
a. How many ways can the quiz be completed by selecting one and only one answer per question?
b. How many ways can the quiz be completed by selecting one and only one answer per question so that every answer is incorrect?
c. If a student selects the answer to each question at random, what is the probability that every answer is incorrect?
d. If a student selects the answer to each question at random, what is the probability that at least one answer is correct?
2. Suppose a family has 8 babies where 3 are boys and 5 are girls.
a. How many ways can the 8 babies be assigned to 8 different cribs (1 per crib)?
b. How many ways can 4 babies be selected from the 8 for a visit to the pediatrician?
c. How many ways can 4 babies be selected for a visit to the pediatrician if 1 is a boy and 3 are girls?
3. An undergraduate student will be randomly selected from the student body of a large state university. Let event A = "the student is enrolled in a math class" and let event B = "the student is enrolled in an English class". Suppose that 55% of students are enrolled in math, 35% are enrolled in math but not English and that 5% are enrolled in neither math nor English.
a. Express the percentages described above as probability statements in terms of events A and B.
b. Find the probability that the student is not enrolled in English. Use proper probability notation.
c. Find the probability that the student is enrolled in math or English (or both). Use proper probability notation.
d. Find the probability that the student is enrolled in both math and English. Use proper probability notation.
e. Determine whether the events A and B are independent using a mathematical definition of independence. Hint: Are A and B' independent?