2. In the laboratory, there are flasks of two sizes (volume $V$ and volume $V / 2$) in a total of 100 pieces, with at least three flasks of each size. The lab assistant randomly selects three flasks in sequence, and fills the first one with an 80% salt solution, the second one with a 50% salt solution, and the third one with a 20% salt solution. Then he pours the contents of these three flasks into one dish and determines the percentage of salt in it. For what minimum number of large flasks $N$ will the event "the percentage of salt in the dish is between $45\%$ and $55\%$ inclusive" occur less frequently than the event "when two fair coins are tossed, one head and one tail appear (in any order)"? Justify your answer. (16 points)
Solution. If $N$ is the number of large flasks in the laboratory, $N=3,4, \ldots, 97$, then $n=100-N$ is the number of small flasks in the laboratory, $n=3,4, \ldots, 97$. For the event $A=\{$ the salt content in the dish is between $45 \%$ and $55 \%$ inclusive $\}$, it is necessary to find the smallest $N$ such that the probability $\mathrm{P}(A)45<N<55$. Therefore, $N_{\min }=46$.

Answer: when $N=46$.