Question

ВЕРОЯТНОСТЬ! ПОМОГИТЕ, ПОЖАЛУЙСТА! В ящике 5 белых и 7 черных шаров. Из нее вынули два шарика. Какова вероятность того, что они будут белыми? С объяснением . Есть ответ (5/33) нужно решение

Answer 1

Всего С(12;2)= 12*11/1*2 = 66 вариантов вытащить шарики.
из них С(5;2)=5*4/1*2=10 вариантов вытащить только белые шарики.
вероятность Р=10/66=5/33

Answer 2

Problem Analysis

In this problem, we are given a box with 5 white balls and 7 black balls. We need to find the probability of drawing two white balls from the box.

Solution

To find the probability, we need to calculate the number of favorable outcomes (drawing two white balls) and the total number of possible outcomes (drawing any two balls).

The number of favorable outcomes can be calculated by selecting 2 white balls out of the 5 available white balls. This can be done using the combination formula:

Number of favorable outcomes = C(5, 2)

Similarly, the total number of possible outcomes can be calculated by selecting any 2 balls out of the total 12 balls in the box:

Total number of possible outcomes = C(12, 2)

The probability of drawing two white balls can then be calculated as:

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

Let's calculate the probability step by step:

Calculation

The number of favorable outcomes: - C(5, 2) = 5! / (2! * (5-2)!) = 5! / (2! * 3!) = (5 * 4) / (2 * 1) = 10

The total number of possible outcomes: - C(12, 2) = 12! / (2! * (12-2)!) = 12! / (2! * 10!) = (12 * 11) / (2 * 1) = 66

The probability of drawing two white balls: - Probability = 10 / 66 = 5 / 33

Therefore, the probability of drawing two white balls from the box is 5/33.

Conclusion

The probability of drawing two white balls from a box containing 5 white balls and 7 black balls is 5/33.