# 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 Remember: The process of learning a person lasts a lifetime. The value of the same knowledge for different people may be different, it is determined by their individual characteristics and needs. Therefore, knowledge is always needed at any age and position.