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

x

012345678P

(

X

=

x

)

P

(

X

=

x

)

0.2230.2560.1910.20.0710.0390.0160.0030.001

1. What is the probability that a randomly selected student changed his or her major at least once?
4. What is the probability that a randomly selected student changed his or her major at most twice?
7. Given that a randomly selected person did change majors, what is the probability that he or she changed majors more than three times?