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Notes on Probability Wake Forest University(笔记概率维克森林大学)
Notes on Probability
Allin Cottrell
1 Probability: the classical approach
The classical approach to probability, which has roots in the study of games of chance, is based on the assumption
that we can identify a class of equiprobable individual outcomes of a random experiment. For example, the
outcomes heads and tails are equiprobable when a fair coin is tossed; the outcomes 1, 2, 3, 4, 5, and 6 are all
equiprobable when a fair die is rolled.
Under these conditions the probability of any event, A, is the number of outcomes that correspond to A, which
we’ll write as nA , divided by the total possible outcomes, n. In other words it’s the proportion of the total outcomes
for which A occurs.
nA
0 P A 1 (1)
n
For example, let A be the event of getting an even number when rolling a fair die. There are three outcomes
corresponding to this event, namely 2, 4 and 6, out of a total of six possible outcomes, so the probability P A
3 1
.
6 2
2 Complementary probabilities
This is simple but important. If the probability of some event A is P A then the probability that event A does not
occur, written P A, must be
P A 1 P A
For example, if the chance of rain for tomorrow is 80 percent, the chance that it doesn’t rain tomorrow must be 20
percent. When trying to compute a given probability, it is sometimes much easier to compute the complementary
probability first, then subtract from 1 to get the desired answer.
This principle can be justified on the classical approach as follows. Let nA denote the number of outcomes
that do
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