Probability Paradox Lab vs とれる。教科書を撮って作るAI暗記カード｜穴埋め・4択クイズ

"With 23 people in a class, what's the chance two share a birthday?" The answer exceeds 50%. Were you surprised? Probability Paradox Lab is an interactive app that lets you experience mathematical paradoxes through simulation — results that feel wrong, yet are mathematically proven. [ HOW IT WORKS ] 1. Make your intuitive guess 2. Run the simulation and see the real result 3. Read the math explanation and understand why Be surprised by the answer. Be surprised again by the explanation. [ FREE THEMES ] Birthday Problem (Free) With just 23 people, the probability of a shared birthday exceeds 50%. Why? Monty Hall Problem (Free) After the host opens a losing door, switching wins 2/3 of the time. Mathematically proven — yet deeply counterintuitive. Two Envelopes Problem (Free) A seemingly valid argument says you should always switch envelopes. Where's the flaw? Coupon Collector Problem (Free) Collecting all 10 kinds takes about 29 pulls on average. Fast at first, then it stalls. [ PREMIUM THEMES ] One-time purchase unlocks 20 more paradoxes and Quiz Mode across all 24 themes (72 questions). No subscriptions, no ads for premium users. Ellsberg Paradox Why do people prefer known odds over unknown ones — even when the math says they're equal? Boy or Girl Paradox "One child is a boy." How does that single fact change the probability? False Positive Paradox A 99%-accurate test says positive for a disease 1% of people have. You're sick with only ~50% odds. Gambler's Fallacy Five heads in a row. Is tails due? Randomness is clumpier than it looks. St. Petersburg Paradox Expected value is infinite, yet you'd pay little to play. Why? Nontransitive Dice (Efron-style) A beats B, B beats C, C beats A. No die is the strongest. Parrondo's Paradox Two losing games, played in alternation, somehow become a winning strategy. Simpson's Paradox A treatment wins in every subgroup — yet loses overall. How? Secretary Problem Interview one at a time with no going back. The optimal strategy for catching the best. Benford's Law About 30% of naturally occurring numbers start with a 1. A curious statistical bias. Friendship Paradox Your friends have more friends than you — the network bias that makes it true. 100 Prisoners Problem If even one fails, all are executed. Yet one strategy saves everyone about 31% of the time. Survivorship Bias Bullet holes on bombers that came back mark where a plane can be hit and still fly home. Armor the untouched parts. Regression to the Mean Praise and they slip, scold and they improve — not the coaching, just probability swinging back. Gambler's Ruin Even on a perfectly fair coin, the side with the smaller bankroll goes broke almost every time. Buffon's Needle Drop needles on a lined floor and you can measure π. Pólya's Urn Return the color you drew plus one more, and early luck gets locked in forever. The Arcsine Law The fairer the contest, the more one side leads the whole way. A near-even split is the rarest outcome. Bertrand's Paradox "A random chord" has three answers — 1/3, 1/2 or 1/4 — depending on how you define random. The Sleeping Beauty Problem Halfers and thirders. Change what you count and both answers stand. [ PERFECT FOR ] - Math & statistics enthusiasts - Curious minds who love "why?" - Brain teaser & trivia fans - Students and lifelong learners

教科書・ノートを撮るだけ。あとはアプリが、覚えるところまで連れていきます。 「とれる。」は、紙の教材やノートを撮影すると、その場で暗記カードを自動で作ってくれる学習アプリです。カードを作る手間をゼロにして、毎日の復習に集中できます。 ■ 撮るだけでカードができる 教科書やノートを撮ると、文字を読み取って一問一答カードを自動作成。穴埋めカードも作れます。撮って、候補から選んで保存するだけ。 ■ 毎日ちょうどよい量の復習 覚えやすさに合わせて、次に復習する日を自動で調整（間隔反復）。「今日やるべき枚数」だけが届くので、迷わず続けられます。 ■ 続くと、身につく 連続学習日数、学習ヒートマップ、デッキ別の正答率で、積み上がりが一目でわかります。 ■ ぜんぶ、端末の中で 文字認識もカード作成もオフラインで完結。撮った画像は保存しません。アカウント登録も不要です。 ■ こんな方に ・宅建、簿記、FP、IT系などの資格勉強 ・大学受験や高校の勉強 ・英単語などの語学学習 ・カード作りが面倒で続かなかった方 ■ とれる Pro 買い切り、または月額で、次の機能が使えます。 ・カードの自動作成が無制限 ・穴埋めカードの自動作成 ・デッキ・カードが無制限 ・カードの読み上げ学習 ・CSVでの書き出し／取り込み 無料でも、撮影・手動作成・復習・統計はずっとお使いいただけます。 ——— 【サブスクリプションについて】 ・とれる Pro 月額（自動更新／期間1か月）：¥300/月 ・とれる Pro（買い切り）：¥1,800（1回のお支払い） お支払いはApple IDに請求されます。サブスクリプションは期間終了の24時間前までに解約しない限り自動更新されます。購入後はApp Storeのアカウント設定から管理・解約できます。 利用規約（EULA）: https://www.apple.com/legal/internet-services/itunes/dev/stdeula/ プライバシーポリシー: https://akiaki1984-alt.github.io/app-legal/toreru/privacy/