Answer to Question #142395 in Statistics and Probability for victory

Question #142395

Theorems of addition of probability and theorems of multiplication of probabilities are used for solving
1. There are 30 students in the group. The marks for the control test were the
following: 8 students received “excellent” marks, 12 students - “good” marks, 8
students – “satisfactory”. What is the probability that 3 students invited for answer have “good” marks?

Expert's answer

P(3 students have "good") = P(1st has "good" AND 2nd has "good" AND 3rd has "good") =

= P(1st has "good") * P(2nd has "good") * P(3rd has "good") = "\\frac{12}{30}\\cdot\\frac{11}{29}\\cdot\\frac{10}{28} = 0.05"