<p style="text-align:justify"><span style="font-size:14px"><strong><span style="color:black">Probability </span></strong><span style="color:black">is a mathematical tool used to study randomness. It deals with the chance of an event occurring. For example, if you toss a </span><strong><span style="color:black">fair </span></strong><span style="color:black">coin four times, the outcomes may not be two heads and two tails. However, if you toss the same coin4,000 times, the outcomes will be close to half heads and half tails. The expected theoretical probability of heads in any one toss is </span><span class="math-tex">\(\frac{1}{2}\)</span>&nbsp;<span style="color:black">or .5. Even though the outcomes of a few repetitions are uncertain, there is a regular pattern of outcomes when there are many repetitions. After reading about the English statistician Karl </span><strong><span style="color:black">Pearson </span></strong><span style="color:black">who tossed a coin 24,000 times with result of 12,012 heads, one of the authors tossed a coin 2,000 times. The results were 996 heads. The fraction&nbsp;</span><span class="math-tex">\(\frac{996}{2000}\)</span>&nbsp;<span style="color:black">is equal to .498 which is very close to .5, the expected probability.</span></span></p>

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<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">The theory of probability began with the study of games of chance such as poker. Predictions take the form of probabilities.</span></span></p>

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<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">To predict the likelihood of an earthquake, of rain, or whether you will get an </span><em><span style="color:black">A </span></em><span style="color:black">in this course, we use probabilities. Doctors use probability to determine the chance of a vaccination causing the disease the vaccination is supposed to prevent. A stockbroker uses probability to determine the rate of return on a client&#39;s investments.</span></span></p>