Question

1 урне 5 красных и 5 чёрных. 2 урне 7 красных и 3 черных. 3 урне 4 красных и 6 черных. На удачу извлечен шар, один из любых, найти вероятность извлечения шара оказался черным

Answer 1

1/3 * (0.5 + 0.3 + 0.6) = 7/15

Answer 2

The Problem

We are given three urns with different distributions of red and black balls:

1. Urn 1 has 5 red balls and 5 black balls 2. Urn 2 has 7 red balls and 3 black balls 3. Urn 3 has 4 red balls and 6 black balls

We need to randomly draw one ball from one of these urns and find the probability that the drawn ball is black.

Solution

Let's think step-by-step:

1. There are a total of 5 + 7 + 4 = 16 balls across the three urns.

2. The number of black balls is: - Urn 1: 5 black balls - Urn 2: 3 black balls - Urn 3: 6 black balls - Total black balls = 5 + 3 + 6 = 14

3. The probability of drawing a black ball from each urn is: - Urn 1: Probability of black = 5/10 = 0.5 - Urn 2: Probability of black = 3/10 = 0.3 - Urn 3: Probability of black = 6/10 = 0.6

4. The probability of drawing from each urn is equal, i.e. 1/3.

5. Using the Law of Total Probability, the overall probability of drawing a black ball is: P(black) = P(black | urn 1) × P(urn 1) + P(black | urn 2) × P(urn 2) + P(black | urn 3) × P(urn 3) = 0.5 × 1/3 + 0.3 × 1/3 + 0.6 × 1/3 = 0.5/3 + 0.3/3 + 0.6/3 = 0.45

Therefore, the probability of randomly drawing a black ball is 0.45.