Question

Ребят, хелп В группе спортсменов два мастера спорта, шесть кандидатов в мастера и восемь перворазрядников. По жребию выбирается четыре спортсмена. Найти вероятность: А. – все четыре выбранные спортсмена оказались кандидатами в мастера спорта; В. – среди выбранных спортсменов хотя бы один оказался кандидатом в мастера спорта; С. – среди выбранных спортсменов оказались два мастера спорта и два кандидата в мастера спорта.

Answer 1

2  - м.с.  ,  6 - к.м.с.  ,  8 - 1р.

$P(A)= \frac{C_6^4}{C_{16}^4} = \frac{C_6^{6-4}}{C_{16}^4} = \frac{6\cdot 5\cdot \; 4!}{2!\; \cdot 16\cdot 15\cdot 14\cdot 13} \approx 0,0082\\\\P(B)= 1-P(\overline {A})=1-\frac{C^4_{2+8}}{C^4_{16}} =1- \frac{C_{10}^4}{C^4_{16}} =1- \frac{10\cdot 9\cdot 8\cdot 7}{16\cdot 15\cdot 14\cdot 13} \\\\\approx 1-0,1154=0,8846\\\\P(C)= \frac{C_2^2\cdot C_6^2}{C_{16}^4} = \frac{1\cdot 6\cdot 5\; \cdot 4!}{2!\; \cdot 16\cdot 15\cdot 14\cdot 13} \approx 0,0082$

Answer 2

Problem Analysis

We are given a group of sportsmen consisting of 2 masters of sports, 6 candidates for master of sports, and 8 first-class athletes. We need to find the probabilities of the following events: A. All four selected athletes are candidates for master of sports. B. At least one of the selected athletes is a candidate for master of sports. C. Two masters of sports and two candidates for master of sports are among the selected athletes.

Solution

To solve this problem, we can use the concept of combinations. The number of ways to choose 4 athletes from a group of 16 can be calculated using the combination formula:

nCr = n! / (r! * (n-r)!)

Where n is the total number of athletes and r is the number of athletes to be chosen.

Let's calculate the probabilities for each event.

A. All four selected athletes are candidates for master of sports.

To calculate the probability of this event, we need to