The urn contains a ball of unknown color with equal probability: white or red. A white and a red ball is dropped into the urn, and after mixing, one ball is drawn at random. Find the probability that balls of the same color remain in the urn?
Н1 – there was a white ball in the urn;
P (H1) = 1/2 = 0.5;
H2 – there was a red ball in the urn;
P (H1) = 1/2 = 0.5.
Random event A – a ball was pulled out at random after a red and white ball was placed in the urn.
Let’s apply the formula of total probability:
P (A) = P (H1) * P (A | H1) + P (H2) * P (A | H2) = 1/2 * 1/2 + 1/2 * 1/2 = 1/4 + 1 / 4 = 1/2;
Let’s apply Bayes’ formula.
P (H1 | A) = P (H1) * P (A | H1) / P (A) = 2/3.
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