Question

В урне 8 белых и 6 черных шаров. Из урны наугад вынимаются 2 шара. Найти вероятность того, что они разного цвета. Помогите пожалуйста) надо срочно

Answer 1

Что бы найти впроятность надо количество положительных результатов делить на общее количество результатов. Тоесть 1/14 =0,07 =7%

Answer 2

Problem Analysis

We have an urn containing 8 white balls and 6 black balls. Two balls are randomly drawn from the urn. We need to find the probability that the two balls are of different colors.

Solution

To find the probability of drawing two balls of different colors, we need to calculate the number of favorable outcomes and the total number of possible outcomes.

Let's consider the two scenarios: 1. Drawing a white ball first and a black ball second. 2. Drawing a black ball first and a white ball second.

Scenario 1: Drawing a white ball first and a black ball second

The probability of drawing a white ball first is 8/14 (since there are 8 white balls out of a total of 14 balls in the urn). After drawing a white ball, there are 13 balls left in the urn, out of which 6 are black. Therefore, the probability of drawing a black ball second is 6/13.

The probability of this scenario is calculated by multiplying the probabilities of the individual events: Probability of scenario 1 = (Probability of drawing a white ball first) * (Probability of drawing a black ball second) = (8/14) * (6/13)

Scenario 2: Drawing a black ball first and a white ball second

The probability of drawing a black ball first is 6/14 (since there are 6 black balls out of a total of 14 balls in the urn). After drawing a black ball, there are 13 balls left in the urn, out of which 8 are white. Therefore, the probability of drawing a white ball second is 8/13.

The probability of this scenario is calculated by multiplying the probabilities of the individual events: Probability of scenario 2 = (Probability of drawing a black ball first) * (Probability of drawing a white ball second) = (6/14) * (8/13)

Total Probability

To find the total probability of drawing two balls of different colors, we need to add the probabilities of the two scenarios: Total probability = Probability of scenario 1 + Probability of scenario 2

Calculation

Let's calculate the probability using the given values:

Probability of scenario 1 = (8/14) * (6/13) = 48/182 Probability of scenario 2 = (6/14) * (8/13) = 48/182

Total probability = Probability of scenario 1 + Probability of scenario 2 = 48/182 + 48/182 = 96/182

Simplifying the fraction, we get: Total probability = 48/91

Answer

Therefore, the probability that the two balls drawn from the urn are of different colors is 48/91.

Please let me know if you need any further assistance.