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**Probability Basics
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Probability of an Event
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The probability of an event is
the number of ways it can occur, divided by the total number of possible
outcomes. Probability is always a number between 0 (no outcomes lead to the
event) and 1(all outcomes lead to the event.) Probability can be expressed as a
percent from 0 to 100. For example, when you flip a coin, the probability of
getting a head is 1 (it can only occur one way) divided by 2 (total possible
outcomes), or 1/2. This may also be expressed as a 50% probability.

**Dependent and Independent Events
**

Two events are independent if
the occurrence of one does not affect the probability of the other. Coin tosses
and the roll of dice are examples of independent events.

Two events are dependent if the
outcome or occurrence of the first changes the probability of the second. For
example, the odds of picking an ace from a shuffled deck of 52 playing cards are
4/52 or 1/13. If the card is not replaced, the odds of picking a second ace are
changed to 3/51. The odds of picking any other particular card are also
affected, because the total number of possible outcomes has changed from 52 to
51.

**Mutually Exclusive Events
**

Mutually exclusive events are
events that can’t happen simultaneously, such as getting both heads and tails
on the same coin toss. When two events are mutually exclusive, the probability
that one or the other will occur is the sum of the probability of each event.
For example, when you roll a six-sided die, the probability of getting either a
3 or a 4 is the sum of the probability of each, or 1/6 + 1/6= 2/6 or 1/3.

**Probability of Multiple Events
**

To find the probability of two
independent events that occur in sequence, multiply the probabilities of the
events occurring separately. For example, the odds of tossing three heads in a
row are ½ x ½ x ½ or 1/8.

**Events vs. Outcomes
**

When you roll a six-sided die,
there are six equally-possible outcomes. Rolling the number four, for example,
is an event that corresponds to the outcome of 4, and therefore has a 1/6 chance
of occurring.

You can combine outcomes to
define different events with different probabilities. For example, when rolling
a six-sided die, an even number is an event that corresponds to three outcomes
(rolling 2, 4 or 6). Therefore the probability is 3/6 or 50%.

**Complement of an Event
**

The complement of an event is the set of all outcomes that
do not lead to the event. If you know the probability of an event, you can find
the probability of its complement by subtracting the probability of the event
from 1. For example, given that the probability of rolling a 5 is 1/6, the
probability of its complement – rolling 1, 2, 3, 4 or 6 – is equal to 1-1/6
or 5/6.