# 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

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