Question

В коробке лежат 3 желтых и 4 красных одинаковых на ощупь кубика наугад вынимают 2 кубика найдите вероятность того что оба кубика окажутся красного цвета

Answer 1

4\7 примерно 57%..................................

Answer 2

Problem Statement

В коробке лежат 3 желтых и 4 красных одинаковых на ощупь кубика. Наугад вынимают 2 кубика. Найдите вероятность того, что оба кубика окажутся красного цвета.

Solution

To find the probability that both cubes will be red, we need to determine the total number of possible outcomes and the number of favorable outcomes.

Total Number of Outcomes

The total number of outcomes is the number of ways we can choose 2 cubes out of the total 7 cubes in the box. This can be calculated using the combination formula:

Total Number of Outcomes = C(7, 2)

Using the combination formula, we can calculate:

C(7, 2) = 7! / (2! * (7-2)!) = 7! / (2! * 5!) = (7 * 6) / (2 * 1) = 21

Therefore, the total number of outcomes is 21.

Number of Favorable Outcomes

The number of favorable outcomes is the number of ways we can choose 2 red cubes out of the 4 red cubes in the box. This can also be calculated using the combination formula:

Number of Favorable Outcomes = C(4, 2)

Using the combination formula, we can calculate:

C(4, 2) = 4! / (2! * (4-2)!) = 4! / (2! * 2!) = (4 * 3) / (2 * 1) = 6

Therefore, the number of favorable outcomes is 6.

Probability Calculation

The probability of both cubes being red can be calculated by dividing the number of favorable outcomes by the total number of outcomes:

Probability = Number of Favorable Outcomes / Total Number of Outcomes

Substituting the values we calculated earlier:

Probability = 6 / 21

Simplifying the fraction:

Probability = 2 / 7

Therefore, the probability that both cubes will be red is 2/7.