B.Sc. (E.C.S.) (Part (Semester (CBCS) Examination, 2018
Probability Theory I (Paper IX)
Day and Date Wednesday, 14-11-2018 Total Marks 70
Time 10.30 a.m. to 1.00 p.m.
Instructions All questions are compulsory.
ii) Figures to the right indicate full marks.
iii) Use of Soundless calculator is allowed.
1. Select most correct alternative 14
If n n
8 7 then value of n is
56 1 15 None of these
A random experiment has possible outcomes.
More than one Less than one
0 None of these
If A and B are independent events with P(A 0.2 0.4. Then

0.2 0.5 1 None of these
A r.v. denoting number of seeds germinated out of 10 planted seeds follows
distribution.
Binomial Poisson
Hyper geometric Uniform
A probability distribution for that mean is always greater than variance is
distribution.
Binomial Poisson Uniform All of these
If A and B are two events which have no point in common, the events A and
B are
Complementary to each other Independent
Mutually exclusive Dependent
If 1 and 1 then
1 0 1 2
The limiting case of binomial distribution is
Binomial distribution Hyper geometric distribution
Uniform distribution Poisson distribution
If A and B are independent events with 0.50 and 0.25 then
P(A
0.625 0.55 1 0.75
10) If five seeds are planted and total number of seeds germinated are recorded
after a week then sample space is

None of these
11) If X and Y denotes numbers on uppermost faces when two fair dice are
thrown together then P(X
3/36 6/36 12/36 1/36
12) Variance of a constant is always
Zero Constant itself
1 None of these
13) An unbiased coin is tossed. Let A getting Head, B getting Tail, then events
A and B are
Mutually exclusive Equally likely
Exhaustive All of these
14) Multiplication principle of counting provides number of ways in which
operations can be done sequentially.
One of the Some of the
All of the None of these
2. Attempt any four 8
Give the axiomatic definition of probability.
Define Poisson distribution.
State multiplication principle of counting.
The p.m.f. of discrete r.v. X is given below. Find value of k.
X 0 1 2 3 4
K 2k 5k 2k k
If X → B 0.5). Calculate S.D. of r.v.X.
Attempt any two 6
Define discrete uniform distribution and give a real life situation where
this distribution is applied.
In how many ways 2-digit numbers can be formed using the digits
9 if repetition is not allowed
Given 0.50, 0.60 P 0.9. Find P(A
P(Ac).
3. Attempt any two 8
An unbiased coin is tossed and a fair die is rolled. If A {Tail} and
B then verify whether the events A and B are independent.
For the following probability distribution of a discrete r,v.X. Find
X 2 4 6 8 10
0.3 0.1 0.2 0.3 0.1
Show that 1 where Ac is complement of A.
Attempt any one 6
State and prove addition law of probability.
Define c.d.f. and state its properties.
4. Attempt any two 10
Let X be Poisson variate with parameter m if P[X 3/10 P[X
find P(X 3).
If three unbiased coins are tossed simultaneously. Let X denotes number
of times head appeared. Find p.m.f of X hence c.d.f of X and obtain
P[X 2].
Attempt any one 4
Show that probability of any event A on sample space always lies between
0 and 1.
If X → B 0.45). Find P(X 7).
5. Attempt any two 14
Define hyper geometric distribution. State its mean and variance. State the
condition under which it is applicable.
An unbiased coin is tossed 3 times. Let B and C are the events that head
occurs at 1st, 2nd and 3rd toss respectively. Discuss the independence of
the events B and C.
A box contains 8 white balls and 6 black balls. Two balls are drawn at random
one by one without replacement. Find the probability of drawing both white
balls first white and second black balls.