Page 269 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Quantitative Techniques – I

Notes 3. (a) The probability of simultaneous occurrence of the two events A and B is given by:
P A  B P A .P B A or P B .P A B
/
/
(b) If A and B are independent P A  B P A .P B .

12.5 Keywords

Combination: When no attention is given to the order of arrangement of the selected objects, we
get a combination.
Counting techniques or combinatorial methods: These are often helpful in the enumeration of
total number of outcomes of a random experiment and the number of cases favourable to the
occurrence of an event.
Equally likely outcomes: The outcomes of random experiment are said to be equally likely or
equally probable if the occurrence of none of them is expected in preference to others.
Expected Monetary Value: When a random variable is expressed in monetary units, its expected
value is often termed as expected monetary value and symbolized by EMV.

Expected Value: Expected value of a constant is the constant itself, i.e., E(b) = b, where b is a
constant.
Mutually exclusive outcomes: Two or more outcomes of an experiment are said to be mutually
exclusive if the occurrence of one of them precludes the occurrence of all others in the same trial
i.e. they cannot occur jointly.
Permutation: A permutation is an arrangement of a given set of objects in a definite order. Thus
composition and order both are important in a permutation

Priori’ definition of probability: If n is the number of equally likely, mutually exclusive and
exhaustive outcomes of a random experiment out of which m outcomes are favourable to the
occurrence of an event A, then the probability that A occurs, denoted by P(A).

Random phenomenon: A phenomenon or an experiment which can result into more than one
possible outcome, is called a random phenomenon or random experiment or statistical
experiment.

12.6 Review Questions

1. Define the term ‘probability’ by (a) The Classical Approach, (b) The Statistical Approach.
What are the main limitations of these approaches?
2. Discuss the axiomatic approach to probability. In what way it is an improvement over
classical and statistical approaches?

3. Explain the meaning of conditional probability. State and prove the multiplication rule of
probability of two events when (a) they are not independent, (b) they are independent.
4. Explain the concept of independence and mutually exclusiveness of two events A and B. If
A and B are
5. Explain the meaning of a statistical experiment and corresponding sample space. Write
down the sample space of an experiment of simultaneous toss of two coins and a die.

6. What is the probability of getting exactly two heads in three throws of an unbiased coin?
7. What is the probability of getting a sum of 2 or 8 or 12 in single throw of two unbiased
dice?

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