There are two identical urns. The first contains 2 black and 3 white balls, the second – 2 black and 1 white balls

There are two identical urns. The first contains 2 black and 3 white balls, the second – 2 black and 1 white balls. First, an urn is randomly chosen, and then one ball is randomly taken from it. What is the probability that a white ball will be selected?

1. We consider the following events and hypotheses:
• A = {white ball extracted from an arbitrary urn};
• H1 = {the ball belongs to the first ballot box}, P (H1) = 1/2 = 0.5;
• H2 = {the ball belongs to the second ballot box}, P (H2) = 1/2 = 0.5;
2. The conditional probability that the white ball belongs to the first urn PH1 (A) = 3 / (2 + 3) = 3/5, and the conditional probability that the white ball belongs to the second urn PH2 (A) = 1 / (2+ 1) = 1/3;
3. By the formula of total probability, we obtain P (A) = P (H1) * RN1 (A) + P (H2) * RN2 (A) = 0.5 * 3/5 + 0.5 * 1/3 = 3 / 10 + 1/6 = 7/15 ≈ 0.47

Remember: The process of learning a person lasts a lifetime. The value of the same knowledge for different people may be different, it is determined by their individual characteristics and needs. Therefore, knowledge is always needed at any age and position.