1. A pigpen contains 7 male pigs and 4 female pigs. Three pigs are randomly drawn (w/o replacement).
a. What is the total number of samples (sequences) in which the first and last pigs drawn will be males (the second pig can be male or female).
b. What is the probability that all three pigs drawn will be female?
2.Suppose that in a large company, 30% of the computers are infected by adware. If 6 computers are randomly
selected and tested, what is the probability that 2 of the computers are infected by adware?
3. Let A = {1, 3, 5, 7, 9} be the domain for a function f. The function consists of all pairs that satisfy the equation:
y = (( x - 3) ^2 / 4) where x is any member of A.
a) What is the range of f ?
b) Does this function have an inverse? If so, what is it? If not, explain why not.
4. Let A = {9, 18, 25, 37}. The relation R is defined on A as follows:
(x, y) E R if 7 evenly divides (y-x)
Hint: an integer k evenly divides an integer j if the remainder of the division operation is equal to 0.
a. List the ordered pairs in relation R.
b. Is R reflexive? Justify your answer.
c. Is R symmetric? Justify your answer.
d. Is R a function? Justify your answer.