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Kenyatta University Probability and Statistics Notes

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Probability summarized Notes-Kenyatta University
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` Kenyatta University
Course : Bachelor of Commerce
Unit Tittle : Probability

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PROBABILITY
Definition. It’s a value between zero and one inclusive, describing the relative possibility
(chance or likelihood) that an event will occur.
Terms used in probability
Experiment: It’s a process or course of action that results in one of a number of possible
outcomes. The outcome that occurs cannot be predicted with certainty e.g. tossing a coin.
Outcome: It’s a particular result of an experiment e.g. getting a head
Event: it’s a collection of one or more outcomes of an experiment.
Sample space: It’s a list of all possible outcomes of the experiment. The outcomes listed
must be mutually exclusive and exhaustive.
Mutually exclusive events: They are events which cannot occur at the same time i.e. when
one event occurs, none of the other events can occur at the same time.
Independent events: -two events are independent if the occurrence of one event does not
alter the probability of the other event.
Collectively exhaustive: At least one of the events must occur when an experiment is
conducted.
Approaches to Assigning Probability
There are three approaches to probability
(a) Classical probability: It’s based on the assumption that the outcomes of an experiment are
equally likely.
Probability of an event =
outcomes possible ofnumber Total
outcomes favourable ofNumber
(b) Empirical probability: the probability of an event occurring is determined by observing
what fraction of the time similar events happened in the past. Probability is based on relative
frequencies.
Probability of an event =
nsobservatio ofnumber Total
past in the occuredevent the timesofNumber
(c) Subjective probability: The likelihood of a particular event happening is assigned by an
individual based on whatever information is available.
Rules for Computing Probabilities
1. Rule of addition
If two events A and B are mutually exclusive, the probability of one or the other event’s
occurring equals the sum of their probabilities.
)()()Bor A ( BPAPP +=
If the two events are not mutually exclusive
)B and ()()()Bor A ( APBPAPP +=
Example
In a class of 20 children, 4 of the 9 boys and 3 of the 11 girls are in the athletics team. A person
from the class is chosen to be in the ‘egg and spoon’ race on the sports day. Find the probability
that the person chosen is:-
(a) In the athletics team
(b) Female

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Probability summarized Notes-Kenyatta University ` Kenyatta University Course : Unit Tittle : Bachelor of Commerce Probability 1 Probability summarized Notes-Kenyatta University PROBABILITY Definition. It’s a value between zero and one inclusive, describing the relative possibility (chance or likelihood) that an event will occur. Terms used in probability ➢ Experiment: It’s a process or course of action that results in one of a number of possible outcomes. The outcome that occurs cannot be predicted with certainty e.g. tossing a coin. ➢ Outcome: It’s a particular result of an experiment e.g. getting a head ➢ Event: it’s a collection of one or more outcomes of an experiment. ➢ Sample space: It’s a list of all possible outcomes of the experiment. The outcomes listed must be mutually exclusive and exhaustive. ➢ Mutually exclusive events: They are events which cannot occur at the same time i.e. when one event occurs, none of the other events can occur at the same time. ➢ Independent events: -two events are independent if the occurrence of one event does not alter the probability of the other event. ➢ Collectively exhaustive: At least one of the events must occur when an experiment is conducted. Approaches to Assigning Probability There are three approaches to probability (a) Classical probability: It’s based on the assumption that the outcomes of an experiment are equally likely. Number of favourable outcomes Probability of an event = Total nu ...
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