19 A statistics class at Wilmington College has 25 students

19. A statistics class at Wilmington College has 25 students of which 15 are math majors and 10 are business majors. The professor randomly selects five students to work together on a group project. What is the probability that less than three of the students in this group are business majors?

Solution

Probability of less than 3 business players = P ( 0 business player) + P ( one business player ) + P( 2 business player )

                                      = 15C₅/25C₅    + (15C₄*10C₁)/25C₅ + (15C₃*10C₂)/25C₅

                                                ₌ 0.056521   + 0.25691   + 0.38537 = 0.6988 (ans)