Name of the University : North Maharashtra University
Degree : B.Sc
Department : Statistics
Year : I
Name Of The Subject :Probability & Probability Distributions
Document type : Question Bank
Website : nmu.ac.in
Download Model/Sample Question Papers : https://www.pdfquestion.in/uploads/nmu.ac.in/5259-F.%20Y.%20BSc.%20Statistics-Pape%20-%20II.pdf
Probability & Probability Distributions Model Paper :
QUESTION BANK FOR F.Y.B.Sc STATISTICS
PAPER-II
Probability & Probability Distributions
Chapter-1 Sample Space & Events
Related : North Maharashtra University Descriptive Statistics B.Sc Question Bank : www.pdfquestion.in/5255.html
A) Questions for 2 marks
1. Give one example each of deterministic & Non – deterministic experiments.
2. Explain random experiment.
3. Define sample space & give two examples of it
4. Draw Venn diagram of A U B; where A & B are any two events of Ω
5. Draw Venn diagram of A⊂ B and B⊂ A where A & B are any two events of Ω
6. Define an elementary event & a compound event
7. Give two examples of countably infinite sample space.
8. Give one example of sure event & impossible event.
9. Explain mutually exclusive events.
10. Explain mutually exhaustive events.
11. Give example of events, which are mutually exclusive & exhaustive.
12. Let O = {1,2, ……….10}, A is event of even numbers & B is event of the numbers
divisible by 3. What will be A U B & A ∩ B ?
13. When an event is said to be occurred? Explain
14. What do you understand by equally likely events?
15. Consider an experiment of rolling of two dice. Write the event that at least one number 2
will occur on uppermost face.
16. A coin is tossed until first head is obtained. Write down the sample space of this expt.
17. Explain concept of complement of an event by Venn- diagram.
18. Let A, B & C be any three events defined on sample space Ω .
19. Explain by Venn – diagram, simultaneous occurrence of A & B.
20. Explain discrete sample space.
B)Questions for 4 Marks
1. What do you mean by an experiment-
2. Define with example each of the following
i) Sample space ii) Discrete sample space
iii) Event iv) Simple event
3. Write a note on sample space.
4. Explain the concept of mutually exclusive & exhaustive events
5. Explain the concept of relative complementation by way of Venn- diagram & also with a
suitable example.
6. Give four examples each of random & non-random experiments
7. Write down the sample spaces for following experiment. Also state the nature (type) of the
sample spaces.
i) A sample is taken to predict the result of the particular assembly poll.
ii) A three digit number is formed from the 5 distinct numbers, using each digit only
once.
8. Let A, B & C be three events on a sample space Ω
Using the union, intersection symbols, write expressions for the following events
i) Only A occurs ii) Exactly one event occurs
iii) Exactly two events occur iv) A & B occur but not C
9. Distinguish clearly between deterministic & non- deterministic models. Give suitable
examples.
10. List the elements of each of the following sample spaces
i) The set of integers between 1 & 50 divisible by 7.
ii) The set Ω = { x / x2 + 5x – 14 = 0 }
iii) The set of outcomes when a coin is tossed until a tail or three heads appear.
iv) The set Ω = { x / 2x + 4 ≥ 0 and x < -2}
11) From amongst 2000 literate individuals of a city, 60% read the newspaper A, 55% read B
& 20% read neither A nor B. How many individuals read both the newspapers?.
Questions for 6 Marks :
1. Let Ω = {1,2,………,10}, A = {1,3,5,7,9}, B = {1,2,3,4}, C = {3,4,5,6,7}
List the elements of following events
i) (A ∩ B) U C ii) (A U B) ∩ C iii) A ∩ B’
iv) [A ∩ (B ∩ C)’]’ v) (A U B U C)’ vi) (A ∩ B) U (A ∩ C)
2. Explain the ideas of union & intersection of two events of sample space. Draw appropriate
Venn diagram.
3. Give an example of random phenomenon that would be used by
i) a teacher ii) a medical researcher iii) an economist
4. Define sample space. Explain various types of sample spaces giving examples of each.
5. Explain i) Occurrence of an event ii) favorable event
6. Explain with one illustration
i) Complement of an event
ii) Mutually exclusive events
iii) Exhaustive events
7. Three coins are tossed together. Let A: exactly 2 coins show heads & B: At least 2 coins
show heads. List the elements of A, B, A’ & B’. Verify whether A & B are mutually
exclusive.
8. Two dice are rolled. Let A be the event that the sum of the points on the uppermost faces is
odd & B the event that there is at least one 3 shown.
Describe the events- i) A U B ii) A ∩ B III) (A ∩ B’) U A’
List the elements contained in it.
9. A party worker aspires for a seat to the state Assembly. So he decides to keep on trying for
a party ticket until he gets one. Give the sample space for his number of attempts. Also
give subsets to represent the following events.
i) He needs 2 attempts to get the nomination.
ii) He needs not more than 5 attempts to get the nomination