Question

в коробке находится 4 красных и 6 зеленых карандашей. Из нее случайно выпали 3 карандаша. Какова вероятность того, что 2 из них красные?

Answer 1

> Р(ККЗ)=4*3*6/10*9*8 > Р(КЗК)=4*6*3/10*9*8 > Р(ЗКК)=6*4*3/10*9*8 > В сумме: > Р(2К+З)=216/720

Answer 2

И 1 зелёный потаму что зелёных много а красных мало

Answer 3

Problem Analysis

In the given problem, there are 4 red and 6 green pencils in a box. Three pencils are randomly selected from the box. We need to find the probability that 2 of the selected pencils are red.

Solution

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

Total Number of Possible Outcomes: The total number of possible outcomes is the number of ways to select 3 pencils from a total of 10 pencils. This can be calculated using the combination formula:

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

where n is the total number of items and r is the number of items to be selected.

In this case, n = 10 (total number of pencils) and r = 3 (number of pencils to be selected).

Total number of possible outcomes = 10C3 = 10! / (3! * (10-3)!)

Number of Favorable Outcomes: The number of favorable outcomes is the number of ways to select 2 red pencils from the 4 available red pencils and 1 pencil from the 6 available green pencils. This can also be calculated using the combination formula:

Number of favorable outcomes = (number of ways to select 2 red pencils) * (number of ways to select 1 green pencil)

Number of ways to select 2 red pencils = 4C2 = 4! / (2! * (4-2)!)
Number of ways to select 1 green pencil = 6C1 = 6! / (1! * (6-1)!)

Calculating the Probability: The probability of an event is given by the formula:

Probability = Number of favorable outcomes / Total number of possible outcomes

Now, let's calculate the probability.

Calculation

Total number of possible outcomes: ``` Total number of possible outcomes = 10C3 = 10! / (3! * (10-3)!) = 10! / (3! * 7!) = (10 * 9 * 8) / (3 * 2 * 1) = 120 ```

Number of favorable outcomes: ``` Number of ways to select 2 red pencils = 4C2 = 4! / (2! * (4-2)!) = 4! / (2! * 2!) = (4 * 3) / (2 * 1) = 6

Number of ways to select 1 green pencil = 6C1 = 6! / (1! * (6-1)!) = 6! / (1! * 5!) = 6

Number of favorable outcomes = (number of ways to select 2 red pencils) * (number of ways to select 1 green pencil) = 6 * 6 = 36 ```

Probability: ``` Probability = Number of favorable outcomes / Total number of possible outcomes = 36 / 120 = 0.3 ```

Answer

The probability that 2 of the randomly selected pencils are red is 0.3.

Verification

Let's verify the answer using a Python simulation.

import random

red_pencils = 4
green_pencils = 6
total_pencils = red_pencils + green_pencils

num_simulations = 1000000
num_favorable_outcomes = 0

for _ in range(num_simulations):
    selected_pencils = random.sample(range(total_pencils), 3)
    num_red_pencils = sum(1 for pencil in selected_pencils if pencil < red_pencils)
    if num_red_pencils == 2:
        num_favorable_outcomes += 1

probability = num_favorable_outcomes / num_simulations
print("Simulated Probability:", probability)

Running the simulation multiple times, we get results close to the calculated probability of 0.3, which verifies our answer.

Conclusion

The probability that 2 of the randomly selected pencils are red is 0.3.