Question

В коробке 8 ручек — 5 синих и 3 чёрные. Сергей не глядя достаёт из коробки 5 ручек. Найдите вероятность того, что среди них будет 3 синие и 2 чёрные

Answer 1

Р=3/5*2/4*1/3*2/3*1/2=1/18
Ответ 1/18

Answer 2

Problem Analysis

In a box, there are 8 pens, consisting of 5 blue pens and 3 black pens. Sergey randomly takes out 5 pens from the box. We need to find the probability that among the 5 pens, there will be 3 blue pens and 2 black pens.

Solution

To find the probability, we need to calculate the number of favorable outcomes (the number of ways to select 3 blue pens and 2 black pens) and the total number of possible outcomes (the total number of ways to select any 5 pens from the box).

Let's calculate these values step by step:

Step 1: Calculate the number of ways to select 3 blue pens from the 5 available blue pens. This can be calculated using the combination formula:

Number of ways to select 3 blue pens = C(5, 3)

Step 2: Calculate the number of ways to select 2 black pens from the 3 available black pens. This can also be calculated using the combination formula:

Number of ways to select 2 black pens = C(3, 2)

Step 3: Calculate the total number of ways to select any 5 pens from the 8 available pens. This can be calculated using the combination formula:

Total number of ways to select 5 pens = C(8, 5)

Step 4: Calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:

Probability = (Number of ways to select 3 blue pens) * (Number of ways to select 2 black pens) / (Total number of ways to select 5 pens)

Let's calculate these values:

Step 1: Calculate the number of ways to select 3 blue pens: Number of ways to select 3 blue pens = C(5, 3) = 10

Step 2: Calculate the number of ways to select 2 black pens: Number of ways to select 2 black pens = C(3, 2) = 3

Step 3: Calculate the total number of ways to select any 5 pens: Total number of ways to select 5 pens = C(8, 5) = 56

Step 4: Calculate the probability: Probability = (Number of ways to select 3 blue pens) * (Number of ways to select 2 black pens) / (Total number of ways to select 5 pens) = (10 * 3) / 56 = 30 / 56 = 15 / 28

Therefore, the probability that among the 5 pens Sergey takes out, there will be 3 blue pens and 2 black pens is 15/28.

Answer

The probability that among the 5 pens Sergey takes out, there will be 3 blue pens and 2 black pens is 15/28.