Transcript Probability
CHAPTER 40
Probability
Probability
What is Probability?
PROBABILITY is how likely something is to happen.
In any situation, the possible things that can happen are
called OUTCOMES.
An OUTCOME of particular interest is called an EVENT.
Probability And Probability Scale
A probability of 0 means that an event is IMPOSSIBLE
A probability of 1 means that an event is CERTAIN
Calculating Probabilities Using Equally Likely Outcomes
Probabilities can be CALCULATED in situations where each
outcome is EQUALLY LIKELY to occur.
The probability of an event X occurring is calculated using:
P (X) = Number of Favourable Outcomes
Total Number of Possible Outcomes
Probability
In many probability situations items are taken or picked at
RANDOM. This means that any item is equally likely to be
picked.
Estimating Probabilities Using Relative Frequency
Sometimes probabilities CANNOT be calculated using
equally likely outcomes. In such situations probabilities can
be estimated using the idea of RELATIVE FREQUENCY.
It is not always necessary to perform an experiment or make
observations, sometimes the information required can be
found in past records.
The relative frequency of an event is given by:
Relative Frequency = Number of favourable outcomes in experiment/survey
Total number of trials in the experiments/survey
Probability
Mutually Exclusive Events
MUTUALLY EXCLUSIVE EVENTS are events which
CANNOT HAPPEN AT THE SAME TIME.
When A and B are events which cannot happen at the
same time:
P(A or B) = P (A) + P (B)
The Probability Of An Event Not Happening
The events A and not A cannot happen at the same time.
Because either ‘event A’ or ‘event not A’ is certain to
happen:
P (A) + P (not A) = 1
=> P (not A) = 1 – P(A)
Probability
Combining Two Events
When two events take place at the same time all possible
outcomes can be worked out by:
a) Listing all the possible outcomes systematically
b) Using a POSSIBILITY SPACE DIAGRAM
c) Draw a TREE DIAGRAM
Probability
Independent Events
Two events are INDEPENDENT if the outcome of one
event does not affect the outcome of the other event.
When A and B are INDEPENDENT events then the
probability of A and B occurring is given by:
P (A and B) = P (A) x P (B)
This rule can be extended to any number of
INDEPENDENT events. For example:
P (A and B and C) = P (A) X P (B) X P (C)