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B COM (HONS) I PAPER IV- BUSINESS STATISTICS Sample Paper with answers
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Class X Maths SA2 Sample Paper 1 for 2015 Exams
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I. Random experiments and sample space
First we definite ‘experiements’. Experiment means an operation which can produce some well definite outcomes. There are two types of experiments —
(a) Deterministic experiments
(b) Probabilistic experiment or random experiments.
(a) Deterministic experiments : Such experiments which when repeated under identical conditions product the same result/outcome are known as deterministic experiments. Example — Experiments related with scientific or engineering facts.
(b) Probabilistic or Random Experiments :
In such experiments, when repeated under identical conditions, do not yield the same outcome every time are known as probabilistic experiments or random experiments. An outcome in such experiments is generally a part of a set of several possible outcomes.
Example (i) In order to draw sandomly a card from a pack of playing cards one cannot predict the certain outcome of the card. So all outcomes related with drawing cards from a pack of playing cards for a set of all possible outcomes which are known as random experients.
(ii) The second example may be rolling a dice in which are cannot predict a certain outcome.
Elementary Event : Outcomes of a random experiments are elementary event. In other words if a random experiment is performed, then each of its outcomes is known as an elimentary event. Elementary events are also called as simple events.
Example : When a dice are thrown, possible outcomes are
1, 2, 3, 4, 5, 6
Each outcome 1, 2, ........ or 6 is called an elementary event.
• Sample Space : The set of all possible outcomes of a random experiment is called the simple space associated with it and it is generally denoted by S.
y, E1, E2, E3,..... En are possible outcomes (or elimentary events) of a random experiment, then
S = {E1, E2, E3,..... En} is the simple space associated with the given random experiments.
Example 1. Consider an experiment associated with throwing are dice. If six faces of the dice are marked as 1, 2, 3, 4, 5 and 6 then all possible outcomes may be
E1 = 1, E2 = 2, E3 = 3, E4 = 4
E5 = 5 and E6 = 6
So the sample space is given as
S = {E1, E2, ..... E6} = ({1, 2, 3, 4, 5, 6}
Total no. of outcomes = 6
Total no. of elementary events = 6
Example 2. We draw two balls from a bag consisting of 3 red and 4 black balls. If we denote three red balls R1, R2 and R3 and four black balls as B1, B2, B3 and B4. Then the elementary events associated with this experiment are
R1R2 R1R3 R2R3
B1B2 B1B3 B1B4 B2B3 B2B4 B3B4
R1B1 R1B2 R1B3 R1B4
R2R1 R2B2 R2B3 R2B4
R3B1 R3B2 R3B3 R3B4
and the set of all the above elementary events is known as sample space.
Example 3. Consider the experiment of tossing two wins together or a win twice. In this experiment the possible outcomes are
HH HT TH TT
Where H = getting head
T = getting tail
Thus the sample space associated with this experiment is
S = {HH, HT, TH, TT
II. Event And its Occurance :
• Definition of Event : A subset of a sample space associated with a random experiment is called an event.
• Example : Consider the random experiment of throwing a die. Since here all possible outcomes are 1, 2, 3, 4, 5 and 6. So the sample space associated with the random experiment is
S = {1, 2, 3, 4, 5, 6}
Now {1}, {2}, {3}, ..... {4, 5, 6}...... {1, 2, 3, 4, 5, 6} are subsets f S.
Total no. of such subsets of 26 = 64
Thus total number of events associated with S is 64. Each event indicates a particular condition associated with S. For instance a subset = A {2, 4, 6} is a set of such outcomes which is known as getting an even number.
i.e., A = {getting an even number}.
In this example, it is clear that one can 64 types of sets made from S or events associated with S which indicate 64 types of different occurances.
• Occurance of an event : An event A associated to a random experiment is said to occur if any one of the elementary events associated to it is an outcome. Thus if an elementary event E is an outcome of a random experiment and A is an event such that E A then we say that the event A has occured.
B COM (HONS) I PAPER IV- BUSINESS STATISTICS Sample Paper with answers
Keep Checking
Adverstisement
Class X Maths SA2 Sample Paper 1 for 2015 Exams
Class X Maths SA2 Sample Paper 2 for 2015 Exams
To Purchase Sample papers of Hindi/Maths/Science for Class X
Call at 9873786724
I. Random experiments and sample space
First we definite ‘experiements’. Experiment means an operation which can produce some well definite outcomes. There are two types of experiments —
(a) Deterministic experiments
(b) Probabilistic experiment or random experiments.
(a) Deterministic experiments : Such experiments which when repeated under identical conditions product the same result/outcome are known as deterministic experiments. Example — Experiments related with scientific or engineering facts.
(b) Probabilistic or Random Experiments :
In such experiments, when repeated under identical conditions, do not yield the same outcome every time are known as probabilistic experiments or random experiments. An outcome in such experiments is generally a part of a set of several possible outcomes.
Example (i) In order to draw sandomly a card from a pack of playing cards one cannot predict the certain outcome of the card. So all outcomes related with drawing cards from a pack of playing cards for a set of all possible outcomes which are known as random experients.
(ii) The second example may be rolling a dice in which are cannot predict a certain outcome.
Elementary Event : Outcomes of a random experiments are elementary event. In other words if a random experiment is performed, then each of its outcomes is known as an elimentary event. Elementary events are also called as simple events.
Example : When a dice are thrown, possible outcomes are
1, 2, 3, 4, 5, 6
Each outcome 1, 2, ........ or 6 is called an elementary event.
• Sample Space : The set of all possible outcomes of a random experiment is called the simple space associated with it and it is generally denoted by S.
y, E1, E2, E3,..... En are possible outcomes (or elimentary events) of a random experiment, then
S = {E1, E2, E3,..... En} is the simple space associated with the given random experiments.
Example 1. Consider an experiment associated with throwing are dice. If six faces of the dice are marked as 1, 2, 3, 4, 5 and 6 then all possible outcomes may be
E1 = 1, E2 = 2, E3 = 3, E4 = 4
E5 = 5 and E6 = 6
So the sample space is given as
S = {E1, E2, ..... E6} = ({1, 2, 3, 4, 5, 6}
Total no. of outcomes = 6
Total no. of elementary events = 6
Example 2. We draw two balls from a bag consisting of 3 red and 4 black balls. If we denote three red balls R1, R2 and R3 and four black balls as B1, B2, B3 and B4. Then the elementary events associated with this experiment are
R1R2 R1R3 R2R3
B1B2 B1B3 B1B4 B2B3 B2B4 B3B4
R1B1 R1B2 R1B3 R1B4
R2R1 R2B2 R2B3 R2B4
R3B1 R3B2 R3B3 R3B4
and the set of all the above elementary events is known as sample space.
Example 3. Consider the experiment of tossing two wins together or a win twice. In this experiment the possible outcomes are
HH HT TH TT
Where H = getting head
T = getting tail
Thus the sample space associated with this experiment is
S = {HH, HT, TH, TT
II. Event And its Occurance :
• Definition of Event : A subset of a sample space associated with a random experiment is called an event.
• Example : Consider the random experiment of throwing a die. Since here all possible outcomes are 1, 2, 3, 4, 5 and 6. So the sample space associated with the random experiment is
S = {1, 2, 3, 4, 5, 6}
Now {1}, {2}, {3}, ..... {4, 5, 6}...... {1, 2, 3, 4, 5, 6} are subsets f S.
Total no. of such subsets of 26 = 64
Thus total number of events associated with S is 64. Each event indicates a particular condition associated with S. For instance a subset = A {2, 4, 6} is a set of such outcomes which is known as getting an even number.
i.e., A = {getting an even number}.
In this example, it is clear that one can 64 types of sets made from S or events associated with S which indicate 64 types of different occurances.
• Occurance of an event : An event A associated to a random experiment is said to occur if any one of the elementary events associated to it is an outcome. Thus if an elementary event E is an outcome of a random experiment and A is an event such that E A then we say that the event A has occured.
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