Data were collected from a survey given to graduating college seniors on the number of times they had changed majors. From that data, a probability distribution was constructed. The random variable X is defined as the number of times a graduating senior changed majors. It is shown below: x
0 1 2 3 4 5 6 7 8
P
(
X
=
x
)
0.194 0.277 0.214 0.19 0.069 0.04 0.011 0.003 0.002
Answer as a fraction or round the answer off to three decimal places:
What is the probability that a randomly selected student changed his or her major at least once?

What is the probability that a randomly selected student changed his or her major at most twice?

Given that a randomly selected person did change majors, what is the probability that he or she changed majors more than three times?

The resumâ´es of two male applicants for a college teaching position in chemistry are placed in the same file as the resumâ´es of two female applicants. two positions become available, and the first, at the rank of assistant professor, is filled by selecting one of the four applicants at random. the second position, at the rank of instructor, is then filled by selecting at random one of the remaining three applicants. using the notation m2f1, for example, to denote the simple event that the first position is filled by the second male applicant and the second position is then filled by the first female applicant, (a) list the elements of a sample space s; (b) list the elements of s corresponding to event a that the position of assistant professor is filled by a male applicant; (c) list the elements of s corresponding to event b that exactly one of the two positions is filled by a male applicant; (d) list the elements of s corresponding to event c that neither position is filled by a male applicant; (e) list the elements of s corresponding to the event a â© b; (f) list the elements of s corresponding to the event a âş c; (g) construct a venn diagram to illustrate the intersections and unions of the events a, b, and c.