Question

В цехе работают 7 мужчин и 5 женщин. По табельным номерам отобраны 8 человек . Какова вероятность того, что среди отобранных лиц окажутся 3 женщины ?

Answer 1

Всего 5+7=12 человек
р=5/12=0,417 вероятность того, что женщина
по формуле Бернулли получаем
Р(3)=$C_8^30.417^30.583^5=56*0.072*0.067=0.272$

Answer 2

Problem Analysis

We are given that there are 7 men and 5 women working in a workshop. From these individuals, 8 people are selected based on their employee numbers. We need to find the probability that among the selected individuals, 3 of them will be women.

Solution

To solve this problem, we can use the concept of combinations. The total number of ways to select 8 people from a group of 12 (7 men and 5 women) is given by the combination formula:

C(n, r) = n! / (r! * (n-r)!)

Where n is the total number of individuals and r is the number of individuals to be selected.

In this case, we want to find the number of ways to select 3 women from a group of 5 women. So, we can calculate:

C(5, 3) = 5! / (3! * (5-3)!) = 5! / (3! * 2!) = (5 * 4 * 3!) / (3! * 2 * 1) = 10

Therefore, there are 10 ways to select 3 women from the group of 5 women.

Next, we need to find the total number of ways to select 8 people from a group of 12 individuals. Using the combination formula, we can calculate:

C(12, 8) = 12! / (8! * (12-8)!) = 12! / (8! * 4!) = (12 * 11 * 10 * 9 * 8!) / (8! * 4 * 3 * 2 * 1) = 495

Therefore, there are 495 ways to select 8 people from the group of 12 individuals.

Finally, we can calculate the probability of selecting 3 women among the 8 selected individuals by dividing the number of ways to select 3 women by the total number of ways to select 8 people:

Probability = (Number of ways to select 3 women) / (Total number of ways to select 8 people) = 10 / 495 ≈ 0.0202

So, the probability that among the selected individuals, 3 of them will be women is approximately 0.0202.

Answer

The probability that among the 8 selected individuals, 3 of them will be women is approximately 0.0202.