1
GATE ECE 2015 Set 2
+2
-0.6
Let $$\,\,X \in \left\{ {0,1} \right\}\,\,$$ and $$\,\,Y \in \left\{ {0,1} \right\}\,\,$$ be two independent binary random variables. If $$\,\,P\left( {X\,\, = 0} \right) = p\,\,$$ and $$\,\,P\left( {Y\,\, = 0} \right) = q\,\,$$, then $$P\left( {X + Y \ge 1} \right)$$ is equal to
A
$$pq+(1-p)(1-q)$$
B
$$pq$$
C
$$p(1-q)$$
D
$$1-pq$$
2
GATE ECE 2015 Set 1
Numerical
+2
-0
The input $$X$$ to the Binary Symmetric Channel (BSC) shown in the figure is $$'1'$$ with probability $$0.8.$$ The cross-over probability is $$1/7$$. If the received bit $$Y=0,$$ the conditional probability that $$'1'$$ was transmitted is _______.
3
GATE ECE 2014 Set 4
Numerical
+2
-0
Parcels from sender $$S$$ to receiver $$R$$ pass sequentially through two post - offices. Each post - office has a probability $${1 \over 5}$$ of losing an incoming parcel, independently of all other parcels. Given that a parcel is lost, the probability that it was lost by the second post - office is _________.
4
GATE ECE 2014 Set 3
Numerical
+2
-0
A fair coin is tossed repeatedly till both head and tail appear at least once. The average number of tosses required is ________.