# Three examiners take an exam in a certain subject from a group of 30 people, with the first interviewing 6 students

**Three examiners take an exam in a certain subject from a group of 30 people, with the first interviewing 6 students, the second with 3 students, and the third with 21 students (students are selected randomly from the list). The attitude of the three examiners to those who are poorly prepared is different: the chances of such students to pass the exam with the first teacher are 40%, for the second – only 10%, for the third – 70%. Find the probability that a poorly prepared student will pass the exam**

Let us denote by 1 2 3 H, H, H the hypothesis that a poorly prepared student answered the first, second and third examiners, respectively. By the condition of the problem

P1 = 6/30 = 0.2

P2 = 3/30 = 0.1

P3 = 21/30 = 0.7

Let the event A = {poorly prepared student passed the exam}. Then again, in view of the condition of the problem

P1 (A) = 0.4

P2 (A) = 0.1

P3 (A) = 0.7

By the formula of total probability we get:

P (A) = 0.4 * 0.2 + 0.1 * 0.1 + 0.7 * 0.7 = 0.58