Question

В цехе работают 7 мужчин и 3 женщины. По табельным номерам наудачу отобраны 3 человека. Найти вероятность того, что все отобранные лица окажутся мужчины

Answer 1

Вероятность выбора первого мужчины равна 7/(7+3) = 0,7.
Вероятность выбора второго мужчины равна 6/(6+3) = 2/3.
Вероятность выбора третьего мужчины равна 5/(5+3) = 5/8 = 0,625.

Общая вероятность находится путем перемножения этих трех вероятностей, она равна $\frac{2}{3} * \frac{5}{8} * \frac{7}{10} = \frac{7}{24}$ .

Answer 2

Problem Analysis

We are given that there are 7 men and 3 women working in a workshop. From these workers, 3 individuals are randomly selected based on their employee numbers. We need to find the probability that all the selected individuals are men.

Solution

To find the probability, we need to determine the total number of possible outcomes and the number of favorable outcomes.

The total number of possible outcomes is the number of ways to select 3 individuals from a total of 10 workers. This can be calculated using the combination formula:

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

where n is the total number of workers (10) and r is the number of individuals to be selected (3).

Let's calculate the total number of possible outcomes:

nCr = 10! / (3!(10-3)!) = 10! / (3!7!) = (10 * 9 * 8) / (3 * 2 * 1) = 120

Now we need to determine the number of favorable outcomes, which is the number of ways to select 3 men from a total of 7 men. This can also be calculated using the combination formula:

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

where n is the total number of men (7) and r is the number of men to be selected (3).

Let's calculate the number of favorable outcomes:

nCr = 7! / (3!(7-3)!) = 7! / (3!4!) = (7 * 6 * 5) / (3 * 2 * 1) = 35

Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:

Probability = Number of favorable outcomes / Total number of possible outcomes = 35 / 120 = 7 / 24

Therefore, the probability that all the selected individuals will be men is 7/24.