Algebra II: Combinations and Permutations to compute Probability
This is a free lesson from our course in Algebra II
In this section you'll explore how combinations and permutations concepts can be used to compute probabilities. It is explained using some examples with solution, with the help of audio, video presentation and in instructor's own hand writing. Simply saying probability is an estimate of frequency of an outcome in repeated trials. The probability of event A is the number of ways event A can occur divided by the total number of possible outcomes. Probability will always be a fraction, 0, or 1. If an event cannot happen, the probability is 0. If an event is certain to happen, the probability is 1.
Let P(E) = probability of an event E
      n(E) = the number of elements in E
      n(S) = the number of elements in sample space
The relationship is expressed by P(E)= n(E)/ n(S) and 0 = P(E) =1. (More text below video...)
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Other useful lessons:
Computing combinations and permutations
(Continued from above) Remember about probability:
P(E) = 0 in case of no outcome
P(E) = 1 when the event is sample space
P(E) + P(not E) = 1
If P(E) =  p, then P(not E) =  1 - p
In case of probability form of counting principle: If E1 & E2 are independent events, and if P(E1) = p and P(E2) = q, then the probability of both E1 and E2 occurring is p x q. For example: If the letters of the word CABIN are rearranged at random, the theoretical probability that one arrangement chosen at random will begin and end with a vowel is, 1/10.
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