Probability as Area

<p><a href="https://www.prepswift.com/quizzes/quiz/prepswift-probability-as-area" target="_blank">Probability as Area Exercise</a></p><p>I personally think it&#39;s helpful to think of <strong><span style="color:#8e44ad;">Probability as Area</span></strong>.&nbsp;</p> <p><strong><span style="color:#27ae60;">What the hell does that mean?</span></strong></p> <p>Recall that for any event or occurrence, the sum of each individual possibility is $1$, or $100\%$. Think of all of these possibilities making up a rectangle with an area of $1$. For example, a coin flip presents only two possibilities, heads and tails (each having a probability of $\frac{1}{2}$. A roll of a fair die presents six possibilities, each with a probability of $\frac{1}{6}$. Notice that, in both cases, the areas of all possibilities sum to $1$.&nbsp;</p> <center><svg height="147.9357147216797" style=" width:661.8285522460938px; height:147.9357147216797px; background: #FFF; fill: none; " width="661.8285522460938" x="0" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" y="0"> <svg class="role-diagram-draw-area" xmlns="http://www.w3.org/2000/svg"><g class="shapes-region" style="stroke: black; fill: none;"><g class="composite-shape"><path class="real" d=" M364,6.6 L592.04,6.6 L592.04,138.12 L364,138.12 Z" style="stroke-width: 1; stroke: rgb(0, 0, 0); fill: none; fill-opacity: 1;"></path></g><g class="composite-shape"><path class="real" d=" M73,6.6 L301.04,6.6 L301.04,138.12 L73,138.12 Z" style="stroke-width: 1; stroke: rgb(0, 0, 0); fill: none; fill-opacity: 1;"></path></g><g class="arrow-line"><path class="connection real" d=" M186.04,6.12 L186.04,138.12" stroke-dasharray="" style="stroke: rgb(0, 0, 0); stroke-width: 1; fill: none; 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transform="matrix(1,0,0,1,569.6142578125,99.71429443359375)"><path d="M131 331C152 512 241 611 421 665L379 689C283 657 242 637 191 593C88 506 32 384 32 247C32 82 112 -20 241 -20C371 -20 468 83 468 219C468 334 399 409 293 409C216 409 184 370 131 331ZM255 349C331 349 382 283 382 184C382 80 331 13 254 13C169 13 123 86 123 220C123 255 127 274 138 291C160 325 207 349 255 349Z" fill="rgb(74,144,226)" fill-opacity="1" stroke="rgb(74,144,226)" stroke-opacity="1" stroke-width="8" transform="matrix(0.017,0,0,-0.017,0,0)"></path></g></g></g></g><line style="fill:none;stroke-width:0.914286px;stroke:rgb(74, 144, 226);" x1="569.6142578125" x2="578.0999717712402" y1="81.97858625650406" y2="81.97858625650406"></line></g></g></g></svg> </svg></center> <p><strong><span style="color:#27ae60;">What if they don&#39;t sum to $1$?</span></strong></p> <p>For example, imagine the probability that Bob wears a <span style="color:#f1c40f;">yellow</span> shirt on any given day to be $25\%$. That means the prospect of him wearing a <span style="color:#f1c40f;">yellow </span>shirt accounts for $\frac{1}{4}$ of the &quot;area&quot; of all possibilities. Let&#39;s also say the probability that Bob wears a <span style="color:#e74c3c;">red </span>shirt is $50\%$, meaning it accounts for half of the &quot;area&quot; of all possibilties. What about the remaining $25\%$? That is the probability that Bob does <strong><u>NOT</u></strong> wear a yellow red shirt. 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