Page 32 - DMTH404_STATISTICS

Statistics

Notes 2.3 Summary

 When a random experiment has a finite number N of outcomes, the probability of each
outcome would be 1/N. Based on this assumption they developed a probability theory,
which we shall briefly describe in Sec. 6.4. However, this approach has a number of logical
difficulties. One of them is to find a reasonable way of specifying “equally likely
outcomes.”
 Probability theory attempts to quantify such vague statements about the chances being
good or bad, small or large. To give you an idea of such quantification, we describe two
simple random experiments and associate probabilities with their outcomes.

 Let  be a discrete sample space consisting of the points  ,  , . . . , finite or infinite in
1 2
number. Let P{ }, P{ }, . . . be the probabilities assigned to the points  ,  , . . .
1 2 1 2
 A word about our notation and nomenclature is necessary at this stage. Although we say
that P{} is the probability assigned to the point wj of the sample space, it can be also
j
interpreted as the probability of the singleton event {}.
j
In fact, it would be useful to remember that probabilities are defined only for events and
that P{} is the probability of the singleton event {}. This type of distinction will be all
j j
the more necessary when you proceed to study probability theory for non-discrete sample
spaces in Block 3.

2.4 Keywords

Multiplication Rule : If an operation is performed in n ways and for each of these n ways, a
1 1
second operation can be performed in n ways, then the two operations can be performed
2
together in n n ways.
1 2
Addition Rule : Suppose an operation can be performed in n, ways and a second operation can
be performed in n ways. Suppose, further that it is not possible to perform both together. Then
2
the number of ways in which we can perform the first or the second operation in n + n .
1 2
2.5 Self Assessment

1. If P(A) = 0.3, P(B) = 0.4, P(A  B) = 0.4. Then find P(A  B)
(a) –0.1 (b) 0.3
(b) 0.4 (d) 0.2
2. If P(A) = 0.5, P(B) = 0.7, P(A  B) = 0.4. Then find P(A  B)

(a) 0.8 (b) 0.1
(c) 0.3 (d) 0.4
3. If two identical symmetric dice are thrown. Find the probabilities of obtaining 9 total
score of 8.
(a) 5/36 (b) 2/4
(c) 4/36 (d) 6/36

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