(AUTONOMOUS)
B. Tech I Semester Regular/Supplementary Examinations, December 2017
(Regulations: VCE-R15)
PROBABILITY THEORY AND NUMERICAL METHODS
(Common to Computer Science and Engineering, Information Technology
Electrical and Electronics Engineering)
Date: 27 December, 2017 Time: 3 hours Max Marks: 75
Answer ONE question from each Unit
All Questions Carry Equal Marks
Unit I
1. Five men in a company of 20 are graduates. If 3 men selected out of 20 at random, what
is the probability that:
i. They are all graduates
ii. At least one is graduate
7M
A and B throw a pair of dice one after the other and it is agreed that the one who throws
a sum of 9 first wins. Show that the chances of their winning is 9:8.
8M
2. A bag contains 10 white and 15 black balls. Two balls are drawn in succession. What is the
probability that one is black and the other is white?
7M
In a bolt factory, machines manufacture 35% and 40% of the total and of
their output are defective bolts. A bolt is drawn at random from the product
and is found to be defective. What are the probabilities that it was manufactured by:
i. Machine A
ii. Machine B
8M
Unit II
3. In a large institution, 2.28% of employees have income below Rs. 4500 and 15.87% of
employees have income above Rs.7,500 per month. Assuming the distribution of income
is normal, find its mean and standard deviation.
8M
Assuming that one in 80 births is a case of twins, calculate the probability of 2 or more
sets of twins on a day when 30 births occurs by using Binomial distribution.
7M
4. Out of 800 families with 5 children each, how many would you expect to have:
i. 3 boys
ii. 5 girls
iii. Either 2 or 3 boys
Assume equal probability for boys and girls.
7M
The daily wages of 1000 worker men are normally distributed around a mean of Rs.70 and
with standard deviation of Rs.5. Estimate the number of workers whose daily wages will
be:
i. Between Rs.70 and 72
ii. More than Rs. 75
8M
Unit III
5. Using Regula Falsi method, find a root of the equation
6 4 3 x x x 0 upto four decimals.
8M
Using Newton's backward difference formula, compute 1.9 from the following table:
x 1 1.25 1.5 1.75 2
x 0.3679 0.2865 0.2231 0.1738 0.1353
7M
Cont…2

6. Find a cubic Polynomial passing through the Points 12) and 147) using
Lagrange's interpolation.
8M
Find a real root of the equation log cos 0 ex x correct to three decimal places using
Newton Raphson method.
7M
Unit IV
7. Find y and y at x for the following data:
x 1 2 3 4 5 6
y 1 8 27 64 125 216
8M
By the method of least squares, find the curve that best fits the following
data.
x 1 2 3 4 5
y 1.8 5.1 8.9 14.1 19.8
7M
8.
Using Simpson's
1
3
rd



rule, evaluate

6
0 2 1
dx
x and compare with exact value.
7M
Fit a curve of the form bx y ae for the following data.
x 1 2 3 4 5 6
y 1.6 4.5 13.8 40.2 125 300
8M
Unit V
9. Employing Taylor's series method, find an approximate solution for the initial value
problem
dy
x x y y
dx
at x 2.1
7M
By Runge-kutta fourth order method, solve
2 2
2 1
dy y x
y
dx y x



for y(0.2) taking step
length h=0.2
8M
10. Using Modified Euler's method, find an approximate value of y when x 20.2 given
that 10 log 5
dy x
y
dx y



taking step length h=0.2
7M
Compute y at x 0.8 by applying Adams-Bashforth method, given
2 0.02, 0.0795 0.1762
dy
x y y y y and y
dx

8M