問85
頻出度★★☆
問題を解いて解答群の中から正解を選ぶ，ある AI システムがある。このシステムは, 1回の学習の過程を経るごとに, 学習の過程の前後の比較において, 誤り率が5%低下する (前回の誤り率の95%になる)。現在の正解率が30%であるとき, 正解率が35%を超えるためには, 少なくともあと何回の学習の過程が必要か。
令和7年度 ITパスポート試験 問85
テクノロジ系基礎理論 › 応用数学
This question's explanation and your answers so far.
解説
問 85
Incorrectア
After 1 round it is 0.70×0.95=0.665 (error rate 66.5%, accuracy rate 33.5%), still not exceeding 35%. If you misinterpret the 5% drop in error rate as “the accuracy rate rises by 5 points (30%→35%)”, 1 round may seem enough, but even then the accuracy rate would be exactly 35%, which does not satisfy “exceeds”. In reality it is a proportional decrease of multiplying by 95% of the previous value, so the accuracy rate after 1 round is only 33.5%, which is insufficient.
- イ
正解 The key is to rephrase “accuracy rate exceeds 35%” as “error rate falls below 65%”. The current accuracy rate is 30%, so the error rate is 70% (=0.70). Each round of learning makes the error rate 95% of the previous value (×0.95). The error rate after n rounds is 0.70×0.95ⁿ. After 1 round it is 0.70×0.95=0.665 (=66.5%), so the error rate is still 65% or more and the accuracy rate is 33.5%, not exceeding 35%. After 2 rounds it is 0.70×0.95²=0.70×0.9025=0.63175 (=63.175%), so the error rate falls below 65% for the first time and the accuracy rate becomes 36.825%, exceeding 35%. Therefore at least 2 rounds are needed, and the correct answer is イ.
Incorrectウ
After 2 rounds the error rate is already 63.175% (accuracy rate 36.825%), satisfying the condition, so for a question asking the minimum “at least how many rounds”, 3 is too many.
Incorrectエ
Since 2 rounds are enough to satisfy the condition, 4 rounds are unnecessary. This is a choice that overestimates the number of rounds; the minimum number is 2 rounds.
ここがポイント
- The accuracy rate and error rate are complementary (accuracy rate + error rate = 100%). Think of “accuracy rate exceeds 35%” by replacing it with “error rate falls below 65%”.
- The error rate becomes “95% of the previous value” each time = geometric decrease. Find the error rate after n rounds using 0.70×0.95ⁿ, and compute step by step to find the smallest n that makes it fall below 65%.
用語