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DR. BABASAHEB AMBEDKAR TECHNOLOGICAL UNIVERSITY,
LONERE – RAIGAD – 402 103
Summer Semester Examination, May – 2019


Branch: B. Tech. (CE / CSE / CS)
Semester: IV
Subject with Subject Code: Probability and Statistics [BTCOC402]
Date: 16 / 05 / 2019
Marks: 60
Time: 3 Hrs.
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Instructions: 1] Attempt any 5 Questions from Q. No. 1 to Q. No. 6.
2
3
4
] Figures / structures to the right indicate full marks.
] Assume suitable data, if necessary and mentioned it clearly.
] Neat diagrams must be drawn wherever necessary.
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Q. No. 1 Solve the following questions:
A)
A box contains 3 red and 7 white balls. One ball is drawn at random and its place a ball of other [3]
color is put in the box. Now the ball is drawn at random from the box. Find the probability it is
of red color.
B)
The probability that a management trainee will remain with the company is 0.6. The [3]
probability that an employee earn more than Rs. 10,000 per month is 0.50. The probability
that an employee is a management trainee who remained with the company or who earns
more than Rs. 10,000 per month is 0.70. What is the probability that an employee earns more
than Rs. 10,000 per month, given that he is a management trainee who stay with the
company?
C)
A piece of equipment will function only when all the three components A, B and C are working. [3]
The probability that A failing over one year is 0.15, that of the B failing is 0.05 and that of the C
failing is 0.10. What is the probability that equipment will fail before the end of one year?
D)
In a class of 75 students, 15 were considered to be very intelligent, 45 as medium and the rest [3]
below average. The probability that a very intelligent student fails in vivavoce examination is
0
.005; the medium student failing has probability 0.05; and corresponding probability for a
below average student is 0.15. If a student is known to have passed the vivavoce examination,
what is the probability that he is below average?
Q. No. 2 Attempt any THREE of the Followings:
A)
For any Three random variables X1, X2, X3 show that:
Cov(X1 + X2, X3) = Cov(X1, X3) + Cov(X2, X3)
[4]
[4]
B)
C)
Find the variance of the number obtained on a throw of an unbiased die.
An urn contains 7 white and 3 red balls. Two balls are drawn together, at random, from this [4]
urn. Compute the probability that neither of them is white. Find also the probability of getting
one white and one red ball. Hence compute the expected number of white balls drawn.
D)
A die is tossed twice. Getting ‘a number greater than 4’ is considered a success. Find the mean [4]
and variance of the probability distribution of number of successes.
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