F.Y B.COM
SEMESTER - I
MID SEMESTER EXAMINATION
ELEMENTS OF STATISTICS
MCQS = UNIT - 3
1. Which of the following is not objective approach of probability?
a) Classical
b) Empirical
c) Axiomatic
d) Modern
2. Which of the following statement is true for classical approach?
a) All outcomes of experiment are not equally likely
b) All outcomes of experiment are mutually exclusive and exhaustive.
c) Total outcomes of experiment may be infinite.
d) Experiment should be performed large number of times under essentially identical and homogenous conditions.
3. Exactly one of the event A or B occur can be symbolically written as
a) AÈB
b) (AÈB)-(AÈB)
c) (AÈB)’
d) A’ÈB’
4. Two events A and B are independent if
a) Events A and B do not occurs simultaneously
b) Occurrence of any one is not affected by occurrence of other
c) Their total outcomes result in sample space of experiment.
d) Their intersection is null set.
5. Which of the following is not true for Axiomatic Approach of probability?
a) P(A)³0
b) P(S)=1
c) P(AÈB)=P(A)+P(B)
d) P(A)£1
6. The conditional probabilities P(E1 | A), P(E2 | A), …, P(En | A), which are computed after conducting the experiment, viz., occurrence of A are termed as ________ probabilities.
a) Priori probability
b) Bayes probability
c) Posteriori probability
d) Discrete probability
7. The probabilities P (E1), P(E2), … , P(En) which are already given or known before conducting an experiment are termed as _______probabilities.
a) Priori probability
b) Bayes probability
c) Posteriori probability
d) Discrete probability
8. Two or more events are said to be _______ if the happening of any one of them excludes the happening of all others in the same experiment.
a) exhaustive
b) mutually exclusive
c) independent
d) dependent
9. Events are said to be ________if happening of any one of them is not affected by and does not affect the happening of any one of others.
a) exhaustive
b) mutually exclusive
c) independent
d) dependent
10. Let A and B be the two possible outcomes of an experiment and suppose P(A) = 0·4, P (A ∪ B) = 0·7 and P(B) = 0.3 then event A and B are
a) exhaustive
b) mutually exclusive
c) independent
d) dependent
11. Let A and B be the two possible outcomes of an experiment and suppose P(A) = 0·4, P (A ∪ B) = 0·7 and P(B) = 0.5
then event A and B are
a) exhaustive
b) mutually exclusive
c) independent
d) dependent
12. Two events A and B are mutually exclusive: P(A) = 1/5 and P(B) = 1/3. Find the probability that : Either A or B will
occur
a) 8/15
b) 7/15
c) 1/15
d) 2/15
13. If a bag contains balls of different sizes and experiment is to select a ball at random, all the balls have ______
a) equal probability of being selected
b) different probability of being selected
c) equal probability 0.5 of being selected
d) equal probability 0.1 of being selected
14. If a random experiment results in N exhaustive, mutually exclusive and equally likely outcomes (cases) out of which m are favorable to the happening of an event A, then the probability of occurrence of A, usually denoted by P(A) is given by :P(A) = m/N. This is ________approach of probability.
a) Classical
b) Axiomatic
c) Relative frequency
d) Statistical
15. Which of the following is not true for Empirical probability approach?
a) According to Empirical approach to probability an experiment is performed repeatedly under essentially
homogeneous and identical conditions,
b) According to Empirical approach to probability the limiting value of the ratio of the number of times the
event occurs to the number of trials, as the number of trials becomes indefinitely large, is called the
probability of happening of the event,
c) According to Empirical approach to probability the ratio of the number of times the event occurs to the
number of trials, has finite and unique limit.
d) According to Empirical approach to probability all the outcomes of experiment are equally likely.
16. If events B1, B2, …, Bn are exhaustive events of the sample space S and A be any event from the same sample space, such that P(A) > 0 then ∑ P(Bi /A) =
a) 0
b) P(B1).P(B2)….P(B3)
c) 1
d) P(B1)+P(B2)+…+P(Bn)
17. Let A and B are two dependent events such that event B occur first and then event A occur then multiple rule of probability is
a) P(AÇB)= P(B) P(A/B)
b) P(AÇB)= P(A) P(B/A)
c) P(AÈB) = P(A)+P(B)
d) P(AÈB) = P(A)+P(B)-P(AÇB)
18. Let A, B and C are independent events then
a) P(AÇBÇC)=P(A)+P(B)+P(C)
b) P(AÇBÇC)=P(A)P(B)P(C)
c) P(AÈBÈC)=P(A)+P(B)+P(C)
d) P(AÈBÈC)=P(A)P(B)P(C)
19. Let A, B and C are mutually exclusive events then
a) P(AÇBÇC)=P(A)+P(B)+P(C)
b) P(AÇBÇC)=P(A)P(B)P(C)
c) P(AÈBÈC)=P(A)+P(B)+P(C)
d) P(AÈBÈC)=P(A)P(B)P(C)
20. For any two events A and B Additive rule of probability is
a) P(AÇB)= P(B) P(A/B)
b) P(AÇB)= P(A) P(B/A)
c) P(AÈB) = P(A)+P(B)
d) P(AÈB) = P(A)+P(B)-P(AÇB)
21. A real valued function define on sample space is called ______
a) Random experiment
b) Variable
c) Random variable
d) Expectation
22. Variance of random variable is_____
a) E(X-E(X))^2
b) E(X-E(X))
c) E(X)^2
d) E(E(X)-X/2))^2
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