1
GATE EE 2014 Set 1
+1
-0.3
A fair coin is tossed $$n$$ times. The probability that the difference between the number of heads and tails is $$(n-3)$$ is
A
$${2^{ - n}}$$
B
$$0$$
C
$${}^n{C_{n - 3}}{2^{ - n}}$$
D
$${2^{ - n + 3}}$$
2
GATE EE 2013
+1
-0.3
A continuous random variable $$X$$ has a probability density function $$f\left( x \right) = {e^{ - x}},0 < x < \infty .$$ Then $$P\left\{ {X > 1} \right\}$$ is
A
$$0.368$$
B
$$0.5$$
C
$$0.632$$
D
$$1.0$$
3
GATE EE 2012
+1
-0.3
Two independent random variables $$X$$ and $$Y$$ are uniformly distributed in the interval $$\left[ { - 1,1} \right].$$ The probability that max $$\left[ {X,Y} \right]$$ is less than $$1/2$$ is
A
$$3/4$$
B
$$9/16$$
C
$$1/4$$
D
$$2/3$$
4
GATE EE 2010
+1
-0.3
A box contains $$4$$ white balls and $$3$$ red balls. In succession, two balls are randomly selected and removed from the box. Given that first removed ball is white, the probability that the $$2$$nd removed ball is red is
A
$$1/3$$
B
$$3/7$$
C
$$1/2$$
D
$$4/7$$
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