Chapter 10 Probability
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Simple Probability
Probability of independent event
Theoretical Vs. Experimental Probability
Probability of Compound Events
Conditional probability
Simple Probability:
Probability is the chance or likelihood that an event will happen. It is the ratio of the number of
ways an event can occur to the number of possible outcomes.
Formula:
# 𝑜𝑓 𝑤𝑎𝑦𝑠 𝑎 𝑐𝑒𝑟𝑡𝑎𝑖𝑛 𝑜𝑢𝑡𝑐𝑜𝑚𝑒 𝑐𝑎𝑛 𝑜𝑐𝑐𝑢𝑟
𝑇𝑜𝑡𝑎𝑙 𝑃𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑂𝑢𝑡𝑐𝑜𝑚𝑒𝑠 (𝑆𝑎𝑚𝑝𝑙𝑒 𝑆𝑝𝑎𝑐𝑒)
Example:
http://www.algebra-class.com/examples-of-probability.html
Probability of Independent event
Two events, A and B, are independent if the outcome of A does not affect the outcome of B.
In many cases, you will see the term, "With replacement". As we study a few probability
problems, I will explain how "replacement" allows the events to be independent of each other.
Example:
http://www.algebra-class.com/probability-problems.html
Theoretical Probability VS Experimental Probability:
Theoretical probability is the probability that is calculated using math formulas. This is the probability
based on math theory.
Experimental Probability
Experimental probability is calculated when the actual situation or problem is performed as an
experiment. In this case, you would perform the experiment, and use the actual results to
determine the probability.
In order to accurately perform an experiment, you must:
 Identify what constitutes a "trial".
 Perform a minimum of 25 trials
 Set up an organizer (table or chart) to record your data.
Example:
http://www.algebra-class.com/theoretical-probability.html
Compound Events
Compound events can be further classified as mutually exclusive or mutually inclusive. The
probability is calculated differently for each, so let's first take a look at mutually exclusive events.
When two events cannot happen at the same time, they are mutually exclusive events.
***Mutually Exclusive Events (Events that cannot happen at the same time)***
P(A or B) = P(A) + P(B)
Take note: With this formula, you are adding the probabilites of each event, not multiplying.
Example:
http://www.algebra-class.com/probability-lessons.html
***When two events can occur at the same time, they are inclusive.***
Inclusive Events (Events that CAN happen at the same time)
P(A or B) = P(A) + P(B) - P(A and B)
Example:
http://www.algebra-class.com/probability-lessons.html
Conditional Probability
(Resource come from https://www.mathsisfun.com/data/probability-events-conditional.html)
P(B|A) is also called the "Conditional Probability" of B given A.
Formula:
P(B I A) =
𝑝(𝐴 𝑎𝑛𝑑 𝐵)
𝑝(𝐴)
Example: Ice Cream
70% of your friends like Chocolate, and 35% like Chocolate AND like Strawberry.
What percent of those who like Chocolate also like Strawberry?
P(Strawberry|Chocolate) = P(Chocolate and Strawberry) / P(Chocolate)
0.35 / 0.7 = 50%
50% of your friends who like Chocolate also like Strawberry
(Practice) A math teacher gave her class two tests. 25% of the class passed both tests and 42% of
the class passed the first test. What percent of those who passed the first test also passed the
second test?
Solution:
P(Second|First) =
P(First and Second)
0.25
=
= 0.60 = 60%
P(First)
0.42