Page 166 - Engineering Mathematics Workbook_Final

Probability & Statistics
)
−
−
7. A coin is tossed thrice. Let X be the (a) pq + (1 p )(1 q
event that head occurs in each of the
first two tosses. Let Y be the event (b) pq
that a tail occurs on the third toss. Let (c) (1p − ) q
Z be the event that two tails occur in
−
three tosses. Based on the above (d) 1 pq
information which one of the
following statements is TRUE? [GATE-2015-CS-SET-2]

(a) X and Y are not independent 10. The chance of a student passing an
exam is 20%. The chance of student
(b) Y and Z are dependent passing the exam and getting above
90% marks in it is 5%. Given that a
(c) Y and Z are independent
student passes the examination, the

(d) X and Z are independent probability that the student gets above
90% marks is
[GATE-2015]
1 1
8. The input X to the Binary Symmetric (a) (b)
Channel (BSC) shown in the figure 18 4

‘1’ with probability 0.8. The 2 5
crossover probability is 1/7. If the (c) 9 (d) 18
received bit Y = 0, the condition
probability that ‘1’ was transmitted is [GATE-2015-ME-SET-2]
________. 11. A product is an assemble of 5

different components. The product
can be sequentially assembled in two
possible ways. If the 5 components
are placed in a box and these are
drawn at random from the box, then

the probability of getting a correct
sequence is

2 2
(a) (b)
[GATE-2015-CS-SET-1] 5! 5
2 2
0,1
0,1
9. Let X  ( ) and Y  ( ) be two (c) (d)
independent binary random variables. (5 2− )! (5 3− )!
If ( X = ) 0 = p and (Y = ) 0 = q, [GATE-2015 (PI) ]
P
P
then ( X + Y  ) 1 is equal to
P

164