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Birla Institute of Technology & Science, Pilani
Distance Learning Programmes Division
First Semester 2008-2009
Comprehensive Examination (EC-2 Regular)
Course No. : AAOC ZC111Course Title : PROBABILITY &
STATISTICS
Nature of Exam : Open Book
Weightage : 60%
Duration : 3 HoursDate of Exam : 27/09/2008 (FN)
Note:1. Please follow all theInstructions to Candidates given on
the cover page of the answer book.2. All parts of a question should
be answered consecutively. Each answer should start from a fresh
page.3. Leave about one inch margin space on all four sides of the
answersheet.4. Mobile phones and computers of any kind should not
be used inside the examination hall.Q.1 (a). Let A and B be the
events such that ( ) ( ) 40.030.0 == BPandAP . Find
( )BAP if(i) A and B are mutually exclusive events(ii) A and B
are independent events.
Q.1 (b). A number is chosen from the numbers1,2,3,.. 50 at
random. Find the probability
that chosen number is divisible by either 2 or by 5. [4 + 3 =
7]
Q.2 Urn 1 contains 4 white 2 black balls and Urn 2 contains 2
white 2 black balls. One ball istransferred from Urn 1 to Urn 2
then one ball is drawn from Urn 2.
(a) Find the probability that a white ball is drawn from Urn
2.(b) If the ball drawn from Urn 2 is white, find the probability
that the ball transferred
from Urn 1 to Urn 2 was white. [4 + 3 = 7]
Q.3 A factory is producing 1% defective items. 400 items are
chosen from a large lot of itemsproduced by this factory.
(a) Find mean number of defective items among 400 items.(b) Use
Poisson approximation to the Binomial distribution to find the
probability that
number of defective items found among these 400 items is more
than 3. [2 + 4 = 6]
Q.4 (a). In a photographic process, the developing time of
prints is a random variable having
the normal distribution with mean 16 seconds and standard
deviation 2 seconds. Find
the probability that it will take from 14 seconds to 18 seconds
to develop a print.
Q.4 (b). The number of calls received at a telephone booth are
according to Poisson process
averaging 2 calls per minute. Find the probability that the time
between successive
calls arriving at the booth is more then one minute. [4 + 4 =
8]
No. of Pages = 2
No. of Questions = 8
