1
GATE EE 2015 Set 2
+1
-0.3
Two coins $$R$$ and $$S$$ are tossed. The $$4$$ joint events $$\,\,\,\,\,\,{H_R}{H_S},\,\,\,\,{T_R}{T_S},\,\,\,\,{H_R}{T_S},\,\,\,\,{T_R}{H_S}\,\,\,\,\,\,\,$$ have probabilities $$0.28,$$ $$0.18,$$ $$0.30,$$ $$0.24$$ respectively, where $$H$$ represents head and $$T$$ represents tail. Which one of the following is TRUE?
A
The coin tosses are independent
B
$$R$$ is fair, $$S$$ is not
C
$$S$$ is fair, $$R$$ is not
D
The coin tosses are dependent
2
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
$${2^{ - n + 3}}$$
3
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
$$1.0$$
4
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
$$2/3$$
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