Ano: 2024 Banca: CESGRANRIO Órgão: CNU Prova: CESGRANRIO - 2024 - CNU - Bloco 8 - Nível Intermediário
A sector of a company is made up of 11 employees, 4 of whom are trainees and 7 of whom are permanent staff. A group of 5 employees was drawn at random from among the employees in this sector.
What is the probability that the group formed has only one trainee employee?
To calculate the first simplification, if there is only one trainee, then we will have 5 combinations in which one trainee will be the 1st, one combination in which he will be the 2nd, up to the fifth, then we will only do the 1st operation which is equal to the other 5, so the operation will be multiplied by 5.
Operation in which the 1st is a trainee
1) 11 employees 4 are trainees:
4/11
2) 2nd is a worker:
7 are permanent, 11 are the number of workers but 1 has already been chosen so there are 10 for the draw, thus: 7/10
3) 3rd to be chosen - the number of employees to be drawn is now 6 and the total number of employees is 9: 6/9
4) 4th to be chosen - remaining staff 5 and remaining employees 8: 5/8
5) 5th to be chosen - remaining headcount 4 and remaining employees 7: 4/7
5x(4/11)x(7/10)x(6/9)x(5/8)x(4/7) = simplifying = (1/11)x(1/3)x(1)x(5/2)x(4) = (1/11x3)x5x2 = 10/33
Translated with DeepL.com (free version)
Rute Bezerra de Menezes Gondim
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