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SemesterProject2.html
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<html>
<head>
<title>Semester Project 2</title>
<link href="SemesterProjectCSS.css" type="text/css" rel="stylesheet" />
</head>
<body>
<div class="container_24 clearfix">
<div class="article grid_8">
<ul class="navigation">
<li class="links"><a href="SemesterProject1.html">Home</a></li>
<li class="links"><a href="SemesterProject2.html">Probability Rules</a></li>
</ul>
</div>
<div class="article grid_8 pageTitle">
<p class="pageTitle">AP Stats: Probability</p>
</div>
<div class="article grid_8">
<ul class="navigation">
<li class="links"><a href="SemesterProject3.html">Counting Calculator</a></li>
<li class="links"><a href="SemesterProject4.html">Fun Facts</a></li>
</ul>
</div>
</div>
<br />
<div class="container_24 clearfix">
<div class="article grid_24 page2 terms" id="t">
<p>
<b>Terminology:</b> P reads "probabiltiy of."
A and B are events with given probabilities.
A and B are <i>mutually exclusive</i> if they cannot both occur at the same time, in the same outcome.
</p>
</div>
</div>
<br />
<div class="container_24 clearfix">
<div class="article grid_4 page2 A">
<p>P(A)</p>
</div>
<div class="article grid_20 page2 A">
<p>P(A) = ((# of ways A can occur) / (# of possible outcomes)).</p>
</div>
</div>
<br />
<div class="container_24 clearfix">
<div class="article grid_24 page2 A">
<p>
Example: P (heads on a coin flip) = (1 / 2) = .5
</p>
</div>
</div>
<br />
<div class="container_24 clearfix">
<div class="article grid_4 page2 AorB">
<p>P(A <b>or</b> B)</p>
</div>
<div class="article grid_20 page2 AorB">
<p>
If A and B a mutually exclusive, P(A or B) = P(A) + P(B).
If A and B are not mutually exclusive, P(A or B) = P(A) + P(B) - P(A and B).
</p>
</div>
</div>
<br />
<div class="container_24 clearfix">
<div class="article grid_24 page2 AorB">
<p>
Example: P (5 or 6 on a die) = P(5) + P(6) = (1 / 6) + (1 / 6) = (1 / 3).
</p>
</div>
</div>
<br />
<div class="container_24 clearfix">
<div class="article grid_4 page2 AandB">
<p>P(A <b>and</b> B)</p>
</div>
<div class="article grid_20 page2 AandB">
<p>
If A and B are mutually exclusive, P(A and B) = P(A) * P(B).
If A and B are not mutually exclusive, P(A and B) = P(A) * P(B | A).
</p>
</div>
</div>
<br />
<div class="container_24 clearfix">
<div class="article grid_24 page2 AandB">
<p>
Example: A coin is flipped.
If it results in heads, a standard 6-sided die will be used.
If it results in tails, a 20-sided die will be used.
P (tails and 3) = P(tails) * P(3 | tails) = (1 / 2) * (1 / 20) = (1 / 40).
</p>
</div>
</div>
<br />
<div class="container_24 clearfix">
<div class="article grid_4 page2 BgivenA">
<p>P(B <b>|</b> A)</p>
</div>
<div class="article grid_20 page2 BgivenA">
<p>
If B is dependent on A, P(B | A) = (P(A and B) / P(A)).
If B, C, and D (could be more or less outcomes) are all dependent on A, and the only outcomes of A, the same equation can be written as
P(B | A) = P(A and B) / (P(A and B) + P(A and C) + P(A and D)).
</p>
</div>
</div>
<br />
<div class="container_24 clearfix">
<div class="article grid_24 page2 BgivenA">
<p>
Example: Box A has 2 red items and 2 blue items, and box B has 2 red items and 1 blue item.
P(A | red) = (P(red and A) / P(red)) = (P(A) * P(red | A)) / (P(A) * P(red | A)) + (P(B) * P(red | B))
= ((1 / 2) * (1 / 2)) / ((1 / 2) * (1 / 2)) + ((1 / 2) * (2 / 3)) = (1 / 4) / (7 / 12)
= (3 / 7).
</p>
</div>
</div>
<br />
<div class="container_24 clearfix">
<div class="article grid_4 page2 infiniteSeries">
<p><b>Infinite Series</b></p>
</div>
<div class="article grid_20 page2 infiniteSeries">
<p>
If A and B are mutually exlcusive, P(infinite series) = S,
a = probability of first way A can occur,
and r = the common ratio between any two consecutive probabilities of ways in which A can occur,
with the second divided by the first.
S = (a / (1 - r)).
</p>
</div>
</div>
<br />
<div class="container_24 clearfix">
<div class="article grid_24 page2 infiniteSeries">
<p>
Example: Person A has a 1/4 chance of making a basket, and Person B has a 1/3 chance.
Given that B shoots first, what is the probability that A will win?
a = (2 / 3) * (1 / 4) = (1 / 6),
r = (((2 / 3) * (3 / 4) * (2 / 3) * (1 / 4)) / ((2 / 3) * (1 / 4))) = (1 / 2),
therefore S = ((1 / 6) / (1 - (1 / 2))) = (1 / 3).
</p>
</div>
</div>
<script src="SemesterProjectJS1.js"></script>
</body>
<html>