Page 168 - Engineering Mathematics Workbook_Final

Probability & Statistics

17. X and Y are two random independent probability of getting a red ball in the
events. It is known that P(X) = 0.40 next draw is
and ( X  Y C ) 0.7. Which one of
=
P
the following is the value of (a) 65 (b) 67
P ( X  Y ) ? 156 156
79 89
(a) 0.7 (b) 0.5 (c) (d)
156 156
(c) 0.4 (d) 0.3
[GATE-2016 (IN)]
[GATE-2016-CE-SET-2]
21. A fair coin is tossed N times. The
18. Three cards were drawn from a pack probability that head does not turn up
of 52 cards. The probability that they in any of the tosses is
are a king, a queen, and a jack is
 1  N 1 −  1  N 1 −
16 64 (a)   (b) −  
(a) (b)   2     2  
5525 2197    

3 8   1   N   1   N
(c) (d) (c)     (d) 1−    
13 16575  2   2 

[GATE-2016] [GATE-2016 (PI)]

19. A person moving through a 22. Consider the following experiment:
tuberculosis prone zone has a 50%
probability of becoming infected. Step-1: Flip a fair coin twice.
However, only 30% of infected Step-2: If the outcomes are (TAILS,
people developed the disease. What HEADS) the output is Y and stop.
percentage of people moving through
a tuberculosis prone zone remains Step-3: If the outcomes are either
infected but does not show symptoms (heads, heads) or (HEADS, TAILS),
of disease? then output is N and stop.

(a) 15 (b) 33 Step-4: If the outcomes are (TAILS,
TAILS), then go to Step-1.
(c) 35 (d) 37
The probability that the output of the
[GATE-2016]
experiment is Y is (upto two decimal
20. An urn contains 5 red and 7 green places) ________
balls. A ball is drawn at random and [GATE-2016-CS-SET-1]
its colour is noted. The ball is placed
back into the urn along with another 23. Suppose that a shop has an equal

ball of the same colour. The number of LED bulbs of two
different types. The probability of an
LED bulb lasting more than 100

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