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?

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