The random variable X is defined as the number of times a graduating senior changed majors. It is shown below: xx  0 1 2 3 4 5 6 7 8 P(X=x)P(X=x)  0.274 0.292 0.134 0.156 0.088 0.034 0.018 0.003 0.001 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?

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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:

xx  0 1 2 3 4 5 6 7 8
P(X=x)P(X=x)  0.274 0.292 0.134 0.156 0.088 0.034 0.018 0.003 0.001
  1. What is the probability that a randomly selected student changed his or her major at least once?
      

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

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