https://mathofthings.netlify.app/tag/valore-atteso/valore attesoWowchemy (https://wowchemy.com)en-usTue, 07 Jul 2026 00:00:00 +0000https://mathofthings.netlify.app/media/icon_hu6c6ed29f698bb57c24ca81ba64928043_3770_512x512_fill_lanczos_center_3.pnghttps://mathofthings.netlify.app/tag/valore-atteso/https://mathofthings.netlify.app/slides/probabilita-introduzione/Tue, 07 Jul 2026 00:00:00 +0000https://mathofthings.netlify.app/slides/probabilita-introduzione/<section class="mot-hero" data-background-color="#ed6f5c" data-transition="zoom"> <div id="particles-prob-hero" class="bg-particles" style="position: absolute; top: 0; left: 0; width: 100%; height: 100%; z-index: 1;"></div> <p class="mot-kicker" style="color: white; position: relative; z-index: 10;">matematica per il triennio</p> <h1 style="color: white; position: relative; z-index: 10;">Calcolo delle <span class="math-word" style="color: white; font-style: italic;">Probabilità</span></h1> <p class="mot-tagline" style="color: rgba(255,255,255,0.95); font-size: 1.3em; position: relative; z-index: 10;">quando la <em style="font-style: italic; color: white;">fortuna</em><br>incontra la <em style="font-style: italic; color: white;">matematica</em></p> <p class="mot-meta" style="color: rgba(255,255,255,0.9); position: relative; z-index: 10;">prof. Diego Fantinelli &mdash; The Math of Things</p> </section> <hr> <section> <blockquote class="mot-quote"> "Dio non gioca a dadi con l'universo." — Albert Einstein <span class="quote-attr">Ma i matematici sì.</span> </blockquote> </section> <hr> <section class="mot-divider" data-background-color="#ed6f5c" data-transition="zoom" style="color: white;"> <div id="particles-quando" class="bg-particles" style="position: absolute; top: 0; left: 0; width: 100%; height: 100%; z-index: 1;"></div> <h1 class="r-fit-text" style="position: relative; z-index: 10;">QUANDO ACCADE QUALCOSA?</h1> </section> <section> <p class="mot-kicker">il concetto fondamentale</p> <h2>Che cos'è la <em>probabilità</em>?</h2> <p class="mot-def fragment">La probabilità misura quanto è <b>probabile</b> che accada un evento. È un numero tra 0 e 1.</p> <div class="mot-cols fragment" style="margin-top: 1.5rem;"> <div class="mot-col"> <p style="font-size: 0.85em"><b>Evento impossibile:</b></p> <p class="mot-result" style="font-size: 1.2em">P = 0</p> <p style="font-size: 0.75em">Non accade mai</p> </div> <div class="mot-col"> <p style="font-size: 0.85em"><b>Evento certo:</b></p> <p class="mot-result" style="font-size: 1.2em">P = 1</p> <p style="font-size: 0.75em">Accade sempre</p> </div> </div> <p class="fragment" style="font-size: 0.8em; margin-top: 2rem;">$0 \lt P(\text{evento}) \lt 1$ = <b>probabilità che l'evento accada</b></p> </section> <section> <p class="mot-kicker">esperimento 1: il dado</p> <h2>Lanciamo un <em>dado</em>!</h2> <div style="display: flex; justify-content: center; align-items: center; gap: 2rem; margin: 2rem 0;"> <div style="font-size: 4rem; cursor: pointer; user-select: none; padding: 1rem;" id="dice-visual">🎲</div> <div style="text-align: left; font-size: 0.85em;"> <p><b>Spazio campionario:</b></p> <p>$\{1, 2, 3, 4, 5, 6\}$</p> <p style="margin-top: 1rem;"><b>Probabilità di un numero:</b></p> <p class="mot-result">$$P(\text{un numero}) = \frac{1}{6}$$</p> </div> </div> <button id="roll-btn" style="padding: 0.8rem 1.5rem; font-size: 1.1em; background: var(--mot-primary); color: white; border: none; border-radius: 8px; cursor: pointer; font-weight: 600;">Lancia il dado</button> <p id="dice-result" style="margin-top: 1.5rem; font-size: 1.2em; color: var(--mot-primary); font-weight: 600; min-height: 1.5em;"></p> </section> <section> <p class="mot-kicker">la moneta non tradisce</p> <h2>Testa o <em>Croce</em>?</h2> <div style="display: flex; justify-content: center; align-items: center; gap: 2rem; margin: 2rem 0;"> <div style="font-size: 4rem; cursor: pointer; user-select: none; padding: 1rem;" id="coin-visual">🪙</div> <div style="text-align: left; font-size: 0.9em;"> <p><b>Due esiti equiprobabili:</b></p> <p class="mot-result" style="font-size: 1.1em">$$P(\text{Testa}) = P(\text{Croce}) = \frac{1}{2}$$</p> </div> </div> <button id="flip-btn" style="padding: 0.8rem 1.5rem; font-size: 1.1em; background: var(--mot-primary); color: white; border: none; border-radius: 8px; cursor: pointer; font-weight: 600;">Lancia la moneta</button> <p id="coin-result" style="margin-top: 1.5rem; font-size: 1.1em; min-height: 1.5em;"></p> <p class="fragment" style="font-size: 0.75em; margin-top: 1rem; color: #666;">Se la moneta è <b>equa</b>, testa e croce hanno la stessa probabilità.</p> </section> <hr> <section class="mot-divider" data-background-color="#ed6f5c" data-transition="zoom" style="color: white;"> <div id="particles-sondaggi" class="bg-particles" style="position: absolute; top: 0; left: 0; width: 100%; height: 100%; z-index: 1;"></div> <h1 class="r-fit-text" style="position: relative; z-index: 10;">SONDAGGI & STATISTICHE</h1> </section> <section> <p class="mot-kicker">proporzionalità</p> <h2>Il <em>sondaggio</em> della classe</h2> <p class="mot-def">Facciamo un rapido sondaggio: chi preferisce i dadi, chi la moneta, chi l'astrologia?</p> <div style="margin: 1.5rem auto 1rem; width: 95%; max-width: 750px;"> <div style="margin: 0.8rem 0;"> <div style="display: grid; grid-template-columns: 300px 1fr; align-items: center; gap: 1rem; margin-bottom: 1rem;"> <span style="font-weight: 600; text-align: left;">Dadi</span> <div id="bar-dice" style="height: 35px; background: var(--mot-primary); width: 0%; border-radius: 4px; transition: width 0.3s; display: flex; align-items: center; justify-content: flex-end; padding-right: 10px; color: white; font-weight: 600; font-size: 0.95em;"></div> </div> <div style="display: grid; grid-template-columns: 300px 1fr; align-items: center; gap: 1rem; margin-bottom: 1rem;"> <span style="font-weight: 600; text-align: left;">Moneta</span> <div id="bar-coin" style="height: 35px; background: #3a6b8c; width: 0%; border-radius: 4px; transition: width 0.3s; display: flex; align-items: center; justify-content: flex-end; padding-right: 10px; color: white; font-weight: 600; font-size: 0.95em;"></div> </div> <div style="display: grid; grid-template-columns: 300px 1fr; align-items: center; gap: 1rem;"> <span style="font-weight: 600; text-align: left;">Astrologia</span> <div id="bar-astro" style="height: 35px; background: #999; width: 0%; border-radius: 4px; transition: width 0.3s; display: flex; align-items: center; justify-content: flex-end; padding-right: 10px; color: white; font-weight: 600; font-size: 0.95em;"></div> </div> </div> </div> <div style="display: flex; gap: 1rem; justify-content: center; margin: 1.5rem 0;"> <button onclick="voteFor('dice')" style="padding: 0.7rem 1.3rem; background: var(--mot-primary); color: white; border: none; border-radius: 6px; cursor: pointer; font-weight: 600;">Dadi</button> <button onclick="voteFor('coin')" style="padding: 0.7rem 1.3rem; background: #3a6b8c; color: white; border: none; border-radius: 6px; cursor: pointer; font-weight: 600;">Moneta</button> <button onclick="voteFor('astro')" style="padding: 0.7rem 1.3rem; background: #999; color: white; border: none; border-radius: 6px; cursor: pointer; font-weight: 600;">Astrologia</button> </div> <p id="poll-stats" style="margin-top: 1.5rem; font-size: 0.55em; font-family: 'JetBrains Mono', monospace; font-weight: 600; color: var(--mot-primary); min-height: 1.8em;"></p> </section> <hr> <section class="mot-divider" data-background-color="#ed6f5c" data-transition="zoom" style="color: white;"> <div id="particles-gioco" class="bg-particles" style="position: absolute; top: 0; left: 0; width: 100%; height: 100%; z-index: 1;"></div> <h1 class="r-fit-text" style="position: relative; z-index: 10;">IL GIOCO</h1> </section> <section> <p class="mot-kicker">il lotto italiano</p> <h2>Giocare alla <em>lotteria</em></h2> <div class="mot-cols fragment" style="margin-top: 1.5rem;"> <div class="mot-col"> <p style="font-size: 0.9em;"><b>Numero totale:</b></p> <p class="mot-result">90 numeri</p> </div> <div class="mot-col"> <p style="font-size: 0.9em;"><b>Numero estratto:</b></p> <p class="mot-result">1 numero</p> </div> </div> <p class="fragment" style="font-size: 0.85em; margin-top: 2rem;"><b>Qual è la probabilità che vinca il mio numero?</b></p> <p class="fragment mot-result">$$P(\text{vincere}) = \frac{1}{90} \approx 1.1\%$$</p> <p class="fragment mot-joke" style="margin-top: 1.5rem;">È più probabile che il tuo cognato ti presti soldi</p> </section> <section> <p class="mot-kicker">il gioco della roulette</p> <h2>Una <em>roulette</em> equa?</h2> <p class="mot-def fragment">La roulette francese ha 37 numeri (0–36). Se punti su un numero:</p> <div class="fragment" style="margin: 1.5rem 0;"> <p class="mot-result" style="font-size: 1.1em">$$P(\text{vinci}) = \frac{1}{37} \approx 2.7\%$$</p> <p style="font-size: 0.9em; margin-top: 0.5rem;">Ma se vinci, il casinò ti paga solo 35 volte la puntata!</p> </div> <p class="fragment" style="font-size: 0.85em; margin-top: 1.5rem;"><b>Dovrebbe pagarti 36 volte</b> (37 − 1 per la puntata). Lui ne paga solo 35. Ecco il guadagno del casinò!</p> <p class="mot-joke fragment" style="margin-top: 1rem;">Il casinò non è truccato. È matematicamente sleale.</p> </section> <section> <p class="mot-kicker">value & risk</p> <h2>Il <em>valore atteso</em> di un gioco</h2> <p class="mot-def fragment">Il valore atteso è quanto <b>ci aspettiamo di guadagnare (o perdere) in media</b> da un gioco.</p> <p class="fragment" style="font-size: 0.85em; margin-top: 1.5rem;">Esempio: punto 1 euro sulla roulette su un numero:</p> <div class="fragment" style="margin: 1.5rem 0; font-family: 'JetBrains Mono', monospace; font-size: 0.85em;"> <p>Vinci (prob 1/37): guadagni 35 euro</p> <p>Perdi (prob 36/37): perdi 1 euro</p> </div> <p class="fragment mot-result">$$E = \frac{1}{37} \cdot 35 + \frac{36}{37} \cdot (-1) =$$</p> <p class="fragment mot-result">$$= \frac{35 - 36}{37} = -\frac{1}{37} \approx -0.027$$</p> <p class="fragment" style="font-size: 0.85em; margin-top: 1rem;">In media, <b>perdi 2.7 centesimi ogni volta</b> che punti 1 euro. Su 1000 scommesse: 27 euro in meno.</p> </section> <section> <p class="mot-kicker">il verdetto</p> <h2>Gioco <em>equo</em> vs gioco <em>truccato</em></h2> <div class="mot-cols fragment" style="margin-top: 1.5rem;"> <div class="mot-col" style="border-left: 4px solid var(--mot-primary); padding-left: 1rem;"> <p style="font-size: 0.9em; font-weight: 600; color: var(--mot-primary);">GIOCO EQUO</p> <p style="font-size: 0.8em; margin-top: 0.5rem;">Valore atteso = 0</p> <p style="font-size: 0.75em; color: #666;">Non si guadagna né si perde</p> <p style="font-size: 0.75em; color: #666; margin-top: 0.5rem;">Esempio: lanciare una moneta e scommettere</p> </div> <div class="mot-col" style="border-left: 4px solid #c2185b; padding-left: 1rem;"> <p style="font-size: 0.9em; font-weight: 600; color: #c2185b;">GIOCO SLEALE</p> <p style="font-size: 0.8em; margin-top: 0.5rem;">Valore atteso < 0</p> <p style="font-size: 0.75em; color: #666;">Il banco ha vantaggio</p> <p style="font-size: 0.75em; color: #666; margin-top: 0.5rem;">Esempio: roulette, lotto, gratta e vinci</p> </div> </div> </section> <hr> <section class="mot-divider" data-background-color="#ed6f5c" data-transition="zoom" style="color: white;"> <div id="particles-riassunto" class="bg-particles" style="position: absolute; top: 0; left: 0; width: 100%; height: 100%; z-index: 1;"></div> <h1 class="r-fit-text" style="position: relative; z-index: 10;">IL RIASSUNTO</h1> </section> <section> <p class="mot-kicker">in breve</p> <h2>Tre lezioni dalla <em>probabilità</em></h2> <ol style="font-size: 0.95em; line-height: 1.8; text-align: left; display: inline-block;"> <li class="fragment"><b>La probabilità misura la rarità:</b> da 0 (impossibile) a 1 (certo).</li> <li class="fragment"><b>I dadi e le monete sono equi:</b> tutti gli esiti hanno la stessa probabilità.</li> <li class="fragment"><b>Il valore atteso racconta la verità:</b> se è negativo, il gioco è contro di te. 📉</li> </ol> <p class="mot-joke fragment" style="margin-top: 2rem;">La buona notizia: la matematica non mente. La cattiva notizia: il casinò sa bene di mentire.</p> </section> <section class="mot-hero" data-background-color="#ed6f5c" data-transition="zoom" style="color: white;"> <div id="particles-finale" class="bg-particles" style="position: absolute; top: 0; left: 0; width: 100%; height: 100%; z-index: 1;"></div> <h1 style="font-size: 2.5em; color: white; position: relative; z-index: 10;">Il gioco è solo <em style="color: white; font-style: italic;">uno specchio</em></h1> <p style="font-size: 1.2em; margin-top: 1.5rem; color: white; position: relative; z-index: 10;">La probabilità ti insegna a <b>leggere il mondo</b>.</p> <p class="mot-meta" style="color: rgba(255,255,255,0.95); margin-top: 2rem; position: relative; z-index: 10;">Prossima lezione: Calcoliamo le probabilità sul serio</p> </section> <hr> <style> @keyframes flip-coin { 0% { transform: rotateY(0deg) rotateX(0deg); } 50% { transform: rotateY(720deg) rotateX(180deg); } 100% { transform: rotateY(1080deg) rotateX(360deg); } } @keyframes bounce-dice { 0% { transform: translateY(0) rotateX(0deg) rotateY(0deg) rotateZ(0deg); } 25% { transform: translateY(-40px) rotateX(180deg) rotateY(180deg) rotateZ(90deg); } 50% { transform: translateY(-70px) rotateX(360deg) rotateY(360deg) rotateZ(180deg); } 75% { transform: translateY(-40px) rotateX(540deg) rotateY(540deg) rotateZ(270deg); } 100% { transform: translateY(0) rotateX(720deg) rotateY(720deg) rotateZ(360deg); } } #dice-visual { display: inline-block; perspective: 1000px; font-weight: bold; font-size: 2.5em; } #dice-visual.rolling { animation: bounce-dice 0.8s cubic-bezier(0.68, -0.55, 0.265, 1.55); } #coin-visual { display: inline-block; perspective: 1000px; font-weight: bold; font-size: 2.8em; } #coin-visual.flipping { animation: flip-coin 0.8s ease-in-out; } .mot-hero h1 em, .mot-hero .mot-tagline em { color: rgba(255,255,255,0.95); font-style: italic; } /* Particles bianchi su sfondo corallo */ .reveal section[data-background-color="#ed6f5c"] svg line, .reveal section[data-background-color="#ed6f5c"] svg circle { stroke: rgba(255, 255, 255, 0.4) !important; fill: rgba(255, 255, 255, 0.2) !important; } </style> <script src="https://cdn.jsdelivr.net/npm/tsparticles@2.12.0/tsparticles.bundle.min.js"></script> <script> // Particles bianchi su sfondo corallo (function () { if (typeof tsParticles === 'undefined') return; var config = { fpsLimit: 60, particles: { number: { value: 80, density: { enable: true, area: 800 } }, color: { value: '#ffffff' }, opacity: { value: { min: 0.2, max: 0.5 } }, size: { value: { min: 0.5, max: 3 } }, move: { enable: true, speed: { min: 0.2, max: 1.5 }, direction: 'none', random: true, straight: false, outModes: { default: 'out' } } }, interactivity: { events: { onHover: { enable: false }, onClick: { enable: false } } }, detectRetina: true }; // Circular trajectories config.particles.move.spin = { enable: true, acceleration: 0 }; // Carica particles su tutti i div con sfondo corallo var particleIds = ['particles-prob-hero', 'particles-quando', 'particles-sondaggi', 'particles-gioco', 'particles-riassunto', 'particles-finale']; particleIds.forEach(function(id) { var elem = document.getElementById(id); if (elem) { tsParticles.load(id, config); } }); })(); // Sondaggio let pollVotes = { dice: 0, coin: 0, astro: 0 }; function voteFor(option) { pollVotes[option]++; updatePoll(); } function updatePoll() { const total = pollVotes.dice + pollVotes.coin + pollVotes.astro; if (total === 0) return; const pct = (val) => total > 0 ? Math.round((val / total) * 100) : 0; document.getElementById('bar-dice').style.width = (pct(pollVotes.dice) * 0.8) + '%'; document.getElementById('bar-dice').textContent = pct(pollVotes.dice) + '%'; document.getElementById('bar-coin').style.width = (pct(pollVotes.coin) * 0.8) + '%'; document.getElementById('bar-coin').textContent = pct(pollVotes.coin) + '%'; document.getElementById('bar-astro').style.width = (pct(pollVotes.astro) * 0.8) + '%'; document.getElementById('bar-astro').textContent = pct(pollVotes.astro) + '%'; const stats = `Voti totali: ${total} | Dadi: ${pollVotes.dice} (${pct(pollVotes.dice)}%) | Moneta: ${pollVotes.coin} (${pct(pollVotes.coin)}%) | Astrologia: ${pollVotes.astro} (${pct(pollVotes.astro)}%)`; document.getElementById('poll-stats').textContent = stats; } // Dado document.getElementById('roll-btn').addEventListener('click', function() { const diceVisual = document.getElementById('dice-visual'); const result = Math.floor(Math.random() * 6) + 1; diceVisual.classList.remove('rolling'); void diceVisual.offsetWidth; diceVisual.classList.add('rolling'); document.getElementById('dice-result').textContent = ''; setTimeout(() => { diceVisual.classList.remove('rolling'); document.getElementById('dice-result').textContent = 'Risultato: ' + result; }, 800); }); // Moneta document.getElementById('flip-btn').addEventListener('click', function() { const coinVisual = document.getElementById('coin-visual'); const result = Math.random() > 0.5 ? 'Testa' : 'Croce'; coinVisual.classList.remove('flipping'); void coinVisual.offsetWidth; coinVisual.classList.add('flipping'); document.getElementById('coin-result').textContent = ''; setTimeout(() => { coinVisual.classList.remove('flipping'); document.getElementById('coin-result').textContent = 'Risultato: ' + result; }, 800); }); </script>