1. A coin was tossed 2021 times. What is the probability that an even number of "heads" will appear?
Answer: $1 / 2$

Solution: Let $p$ be the probability that an even number of "heads" appeared in the first 2020 tosses, and $q=1-p$ be the probability that an odd number appeared. Then, on the 2021st toss, heads will appear with a probability of $1 / 2$, and the probability will be $\frac{1}{2} q$ or tails, then the probability is $\frac{1}{2} p$. The total probability is $\frac{1}{2} p+\frac{1}{2} q=\frac{1}{2}$