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
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Probability
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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.
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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)
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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)