**PROBABILITY
DEFINITION**

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Life is full of various
events; some are certain; some are impossible; and
some are likely. The concept of probability in mathematics
deals with the third type of events. We are neither
interested in certain events nor impossible events
because their outcomes are known already. For instance,
if today were to be Monday, it is certain that tomorrow
will be Tuesday. Nothing can change that; there is
no point in trying to measure the likelihood or calculating
probability of that happening. Also, if today were
to be Monday, it is impossible that tomorrow will
be Thursday. So, there is no need to measure the chances
of that occurring. However, if an event is likely
to occur, we can measure the chances of that happening
- that is what probability is about. Therefore, probability
can be defined as the likelihood or chances of an
event occurring. Some probability examples include:
the probability that it will rain tomorrow, probability
the stock market will fall tomorrow, probability of
obtaining a score of 4 when a die is rolled, probability
of picking a queen from a pack of playing cards etc.

**MEANING OF
PROBABILITY TERMS**

** EVENTS:**
These are the outcomes of experiments.

**EXPERIMENT:**
This is an act that can be repeated under a given
circumstance.

**OUTCOME:**
This is the result of random experiment.

**RANDOM EXPERIMENT:**
This is an experiment whose outcome cannot be predetermined.

**MUTUALLY EXCLUSIVE
EVENTS:** These are events that cannot occur
simultaneously. This implies that the occurrence of
one event automatically means the non-occurrence of
the other.

**INDEPENDENT
EVENTS:** As the name implies, these are events
that can occur separately or simultaneously. This
implies that the occurrence or non-occurrence of one
event will not affect the other.

**DEPENDENT
EVENTS:** These are events in which the occurrence
or non-occurrence of one event will affect the other
event.

**EQUALLY LIKELY:**
Two or more events are said to be equally likely when
there is the same chance of their occurrence.

**SAMPLE SPACE:**
This is all probable outcomes of an experiment.

**SAMPLE POINT:**
This is a member of the sample space i.e. an outcome.

**SIMPLE EVENTS:**
This relates to the outcome of a single trial.

**COMPOUND EVENTS:**
This is a complex trial which result into many outcomes.

**TYPES OF EVENTS
AND THEIR PROBABILITIES**

**(A) CERTAIN
OR SURE EVENTS**: These are events that will
occur irrespective of the circumstances. For instance,
if today were to be Monday, it is certain that tomorrow
will be Tuesday. That is a sure event. The probability
of a sure event occurring is one (1).

**(B) IMPOSSIBLE
OR NULL EVENTS: **These are events that can
never occur. For example, if today were to be Monday,
it is impossible that tomorrow will be Thursday. The
probability of an impossible event occurring is zero
(0).

**(C) FAILURE
OF COMPLEMENT OF AN EVENT: **This is the non-occurrence
of the event. So, if the probability of an event occuring
is p, the complement of the event or the probability
of the event not occuring is 1 - p. This is because
the probability of an event occuring plus the probability
of the event not occuring is 1.

If the probability that a student will pass an exam
is 1/3; then the probability that the student will
fail or not pass the exam is 1 - 1/3 = 2/3.

Similarly, if the probability of not winning a lottery
is 3/5; the probability of winning the lottery will
be 1 - 3/5 = 2/5.

**(D) MUTUALLY
EXCLUSIVE EVENTS: **Two events are said to
be mutually exclusive if the occurrence of one automatically
implies the non-occurrence of the other. For instance,
if a coin is tossed, it either we have a tail (T)
or a head (H). If we have a tail, it automatically
means that we cannot have a head.

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