Page 201 - Engineering Mathematics Workbook_Final

Probability & Statistics

232. An exam paper has 150 multiple (a) 0.05, 1.87 (b) 1.90, 5.87
choice questions of 1 mark each, with (c) 0.05, 1.10 (d) 0.25, 1.40
each question having for choices.
Each incorrect answer fetches -0.25 [GATE-2007 (PI)]
marks. Suppose 1000 students choose 235. A fair coin is tossed repeatedly till

all their answer randomly with both head and tail appear at least
uniform probability. The sum total of once. The average number of tosses
the expected marks obtained by all required is ___.
the students is
[GATE-2014-EC SET3]
(a) 0 (b) 2550
236. Each of the nine words in the
(c) 7525 (d) 9375 sentence, “The Quick brownfox
jumps over the lazy dog” is written in
[GATE-2004 (CS)]
a separate piece of paper. These nine
233. The following data about the flow of pieces of paper are kept in a box. One
liquid was observed in a continuous of the piece is drawn at random from
chemical process plant. the box. The expected length of the
word drawn is _____.
Frequency
Flow rate
(litres / sec) (The answer should be rounded to
7.5 to 7.7 1 one decimal place)
7.7 to 7.9 5
7.9 to 8.1 35 [GATE-2014 (CS-SET2)]
8.1 to 8.3 17
8.3 to 8.5 12 237. Let the random variable X represent
8.5 to 8.7 10 the number of times a fair coin needs
Mean flow rate of the liquid is to be tossed till two consecutive
heads appear for the first time. The
(a) 8.00 litres / sec (b) 8.06 litres / expectation of X is _____.
sec
[GATE-2005]
(c) 8.16 litres / sec (d) 8.26 litres /
sec 238. Passengers try repeatedly to get a seat
reservation in any train running
[GATE-2004]
between two stations until they are

234. The random variable X takes on the successful. If there is 40% chance of
values 1, 2, (or) 3 with probabilities getting reservation in any attempt by
+
+
+
2 5P 1 3P 1.5 2P a passenger then the average number
, and of attempts that passengers need to
5 5 5
respectively the value of P and E(X) make to get a seat reserved is ____.
are respectively. [GATE-2017 EC SESSION-II]

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