Question

Помогите решить! В урне 10 белых, 15 синих и 25 красных шаров. Найти вероятность того, что а) взятые наугад 2 шара окажутся белого и синего цветов; б) взятые наугад 3 шара окажутся все разными.

Answer 1

Сначала складываешь сколько всего шаров:
10+25+15=50

а) белый и синий цвет значит складываем :

10+15:50=0.5

б)50:50=1

Answer 2

Probability of drawing two balls, one white and one blue, from the urn:

To find the probability of drawing two balls, one white and one blue, from the urn, we can use the concept of combinations.

The total number of balls in the urn is 10 white + 15 blue + 25 red = 50 balls.

The number of ways to choose one white ball out of 10 is C(10, 1) = 10.

The number of ways to choose one blue ball out of 15 is C(15, 1) = 15.

Therefore, the total number of ways to choose one white ball and one blue ball is 10 * 15 = 150.

The total number of ways to choose two balls out of 50 is C(50, 2) = 1225.

So, the probability of choosing two balls, one white and one blue, is 150/1225.

Therefore, the probability is 150/1225 or approximately 0.1224.

Probability of drawing three balls, all of different colors, from the urn:

To find the probability of drawing three balls, all of different colors, from the urn, we can again use the concept of combinations.

The number of ways to choose one white ball out of 10 is C(10, 1) = 10.

The number of ways to choose one blue ball out of 15 is C(15, 1) = 15.

The number of ways to choose one red ball out of 25 is C(25, 1) = 25.

Therefore, the total number of ways to choose one white ball, one blue ball, and one red ball is 10 * 15 * 25 = 3750.

The total number of ways to choose three balls out of 50 is C(50, 3) = 19600.

So, the probability of choosing three balls, all of different colors, is 3750/19600.

Therefore, the probability is 3750/19600 or approximately 0.1913.

I hope this helps! Let me know if you have any further questions.