Question

В коробке 5 синих, 4 красных и 3 зеленых карандаша. Наудачу вынимают 3 карандаша. Какова вероятность того, что все они синие?

Answer 1

1) 5+4+3=12 - карандашей всего
2) 5:12=0,416...,т.е. примерно 42%

Answer 2

Calculating the Probability of Drawing 3 Blue Pencils

To calculate the probability of drawing 3 blue pencils out of the total 12 pencils, we can use the formula for probability:

Probability = (Favorable Outcomes) / (Total Outcomes)

In this case, the favorable outcomes are drawing 3 blue pencils, and the total outcomes are drawing any 3 pencils from the box.

Total Number of Outcomes

The total number of ways to draw 3 pencils from the box can be calculated using the combination formula:

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

Where: - n = total number of pencils in the box - r = number of pencils to be drawn

For this scenario, n = 12 (total pencils) and r = 3 (pencils to be drawn).

Favorable Outcomes

The favorable outcomes are drawing 3 blue pencils from the box. Since there are 5 blue pencils in the box, we can calculate the number of ways to draw 3 blue pencils.

Calculation

Let's calculate the probability step by step:

1. Total Outcomes: Using the combination formula, we can calculate the total number of ways to draw 3 pencils from 12: Total Outcomes = 12C3 = 12! / (3! * (12-3)!)

2. Favorable Outcomes: The number of ways to draw 3 blue pencils from 5: Favorable Outcomes = 5C3 = 5! / (3! * (5-3)!)

3. Probability: Finally, we can calculate the probability using the formula: Probability = Favorable Outcomes / Total Outcomes

Let's calculate the probability using the above steps.

Answer 3

Problem Analysis

In a box, there are 5 blue pencils, 4 red pencils, and 3 green pencils. We randomly select 3 pencils from the box. We need to determine the probability that all 3 selected pencils are blue.

Solution

To find the probability, we need to calculate the ratio of the number of favorable outcomes (selecting 3 blue pencils) to the total number of possible outcomes (selecting any 3 pencils).

The total number of pencils in the box is 5 + 4 + 3 = 12.

The number of ways to select 3 blue pencils from the 5 available blue pencils is given by the combination formula:

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

Where: - n is the total number of items (5 blue pencils) - k is the number of items to be selected (3 blue pencils)

Using this formula, we can calculate the number of ways to select 3 blue pencils from the 5 available blue pencils.

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

Therefore, there are 10 ways to select 3 blue pencils from the 5 available blue pencils.

The total number of ways to select any 3 pencils from the 12 pencils in the box is given by the combination formula:

C(12, 3) = 12! / (3! * (12 - 3)!) = 220

Therefore, there are 220 ways to select any 3 pencils from the 12 pencils in the box.

The probability of selecting 3 blue pencils can be calculated as:

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

Probability = 10 / 220 = 1 / 22

Therefore, the probability that all 3 selected pencils are blue is 1/22.

Conclusion

The probability that all 3 selected pencils are blue is 1/22.