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200 students in a high school senior class are surveyed about what majors they intend to declare in college. Of the 200 students, 80 plan to major in mathematics, 100 plan to major in computer science, and 30 plan to pursue a double major in mathematics and computer science. Using this information, answer each of the following questions. Let M be the event that a randomly selected student plans to major in mathematics and C be the event that a randomly selected student plans to major in computer science. What is P(M), left parenthesis, M, right parenthesis, the probability that a student plans to major in mathematics?

Respuesta :

Edufirst

Answer:

  • P(M) = 0.4

Explanation:

1. Build a two-way frequency table:

To have a complete understanding of the scenary build a two-way frequency table.

  • Column and rows:

                                  Major in math    No major in math  Total

Major in CS

No major in CS

Total

  • 200 students:

                                  Major in math    No major in math  Total

Major in CS

No major in CS

Total                                                                                      200

  • 80 plan to major in mathematics:

                                  Major in math    No major in math  Total

Major in CS

No major in CS

Total                              80                                                   200

  • 100 plan to major in computer science:

                                  Major in math    No major in math  Total

Major in CS                                                                           100

No major in CS

Total                              80                                                   200

  • 30 plan to pursue a double major in mathematics and computer science:

                                  Major in math    No major in math  Total

Major in CS                  30                                                      100

No major in CS

Total                              80                                                    200

  • Complete the missing numbers by subtraction:

                                  Major in math    No major in math  Total

Major in CS                   30                              70                 100

No major in CS                                                                     100

Total                              80                             120                200

                                  Major in math    No major in math  Total

Major in CS                   30                              70                 100

No major in CS             50                              50                 100

Total                              80                             120                200

2. What is P(M), the probability that a student plans to major in mathematics?

  • P(M) = number of students who plan to major in mathematics / number of students

  • P(M) = 80 / 200 = 0.4

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