4. Defective Coins (from 6th grade, 1 point). For the anniversary of the St. Petersburg Mathematical Olympiads, the mint struck three commemorative coins. One coin turned out to be correct, the second coin had two eagles on both sides, and the third coin had tails on both sides. The director of the mint randomly selected one of these three coins and tossed it. An eagle came up. What is the probability that the other side of this coin is also an eagle?
Solution. It is known that heads came up. Therefore, either the first or the second coin was chosen. In total, heads are depicted three times on these coins. In one of these three equally likely cases, tails is on the opposite side of the coin, and in the other two cases, heads are on the opposite side. Answer: $\frac{2}{3}$.