Amsco Integrated Algebra I: The Counting Principle, Sample Spaces, and Probability
 This is a free lesson from our course in Amsco's Integrated Algebra

 This lesson explains the the basics of counting principle and the approach to finding the probability of any two or more independent events. The counting principle: If one activity can occur in any of m ways and, following this, a second activity can occur in any of n ways, then both activities can occur in the order given in m * n ways. For example: Let's say that you want to flip a coin and roll a die. There are 2 ways that you can flip a coin and 5 ways that you can roll a die. There are then 2 x 5 = 10 ways that you can flip a coin and roll a die. Sample space is listing of all the possible outcomes is and is generally denoted by the capital letter S.  (More text below video...)
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 (Continued from above) The sample space for the experiments of flipping a coin and rolling a die are S = { H1, H2, H3, H4, H5, T1, T2, T3, T4, T5}. Thus there are ten possible ways. The counting principle for probability states that E and F are independent events, the probability of event E is m(0 <= m <= 1) and the probability of event F is n(0 <= n <=1). The probability of the event in which E and F can occur jointy is the product m * n. For example: the probability to take any of three buses to get to the train station and then take any of the train with two possible options (the buses and trains arrive at random and are equally likely to arrive) to get to work is 1/6. The video above will explain in detail with the help of several examples.

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