Question

В ящике лежало 20 шаров.Из них 12 белых и 8 черных. Наугад вынимают 2 шара .Какова вероятность того ,что они одного цвета? с решением пж

Answer 1

N = 20* (19/2) = 10 * 19 = 190 - общее число возможных случаев
m1 = 8 * (7/2) = 4 * 7 = 28 - число случаев с выпадением 2-х черных шаров
m2 = 12 * (11/2) = 6 * 7 = 66 - число случаев с выпадением 2-х белых шаров

P1 = m1 / n = 28 / 190 = 0,147 - вероятность появления шаров черного цвета
P2 = m2 / n = 66 / 190 = 0,347 -  вероятность появления шаров белого цвета

Answer 2

Probability of Drawing Two Balls of the Same Color

To find the probability of drawing two balls of the same color, we can use the formula:

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

In this case, the favorable outcomes are drawing two balls of the same color, and the total possible outcomes are drawing any two balls from the box.

Calculation

1. Probability of drawing two white balls: - Number of favorable outcomes: 12 white balls choose 2 - Total number of possible outcomes: 20 balls choose 2

2. Probability of drawing two black balls: - Number of favorable outcomes: 8 black balls choose 2 - Total number of possible outcomes: 20 balls choose 2

Solution

1. Probability of drawing two white balls: - Number of favorable outcomes: $\binom{12}{2}$ - Total number of possible outcomes: $\binom{20}{2}$

The probability can be calculated as: ``` P(white) = (12 choose 2) / (20 choose 2) ```

2. Probability of drawing two black balls: - Number of favorable outcomes: $\binom{8}{2}$ - Total number of possible outcomes: $\binom{20}{2}$

The probability can be calculated as: ``` P(black) = (8 choose 2) / (20 choose 2) ```

Final Answer

The probability of drawing two balls of the same color is the sum of the probabilities of drawing two white balls and two black balls: ``` P(same color) = P(white) + P(black) ```

By calculating the above probabilities, we can find the final probability.