1
GATE EE 2015 Set 1
+2
-0.6
Two players, $$A$$ and $$B,$$ alternately keep rolling a fair dice. The person to get a six first wins the game. Given that player $$A$$ starts the game, the probability that $$A$$ wins the game is
A
$$5/11$$
B
$$1/2$$
C
$$7/13$$
D
$$6/11$$
2
GATE EE 2015 Set 1
Numerical
+2
-0
A random variable $$X$$ has probability density function $$f(x)$$ as given below: $$\,\,f\left( x \right) = \left\{ {\matrix{ {a + bx} & {for\,\,0 < x < 1} \cr 0 & {otherwise} \cr } } \right.\,\,$$\$
If the expected value $$\,\,E\left[ X \right] = 2/3,\,\,$$ then $$\,\,\Pr \left[ {X < 0.5} \right]\,\,$$ is __________.
3
GATE EE 2015 Set 1
+2
-0.6
Given Set $$\,\,\,A = \left\{ {2,3,4,5} \right\}\,\,\,$$ and Set $$\,\,\,B = \left\{ {11,12,13,14,15} \right\},\,\,\,$$ two numbers are randomly selected, one from each set. What is the probability that the sum of the two numbers equal $$16?$$
A
$$0.20$$
B
$$0.25$$
C
$$0.30$$
D
$$0.33$$
4
GATE EE 2015 Set 1
+2
-0.6
The probabilities that a student passes in Mathematics, Physics and Chemistry are $$m, p$$ and $$c$$ respectively. Of these subjects, the student has $$75$$% chance of passing in at least one, a $$50$$% chance of passing in at least two and a $$40$$% chance of passing in exactly two. Following relations are drawn in $$m, p, c:$$
$${\rm I}.$$ $$\,\,\,\,\,\,$$ $$p+m+c=27/20$$
$${\rm I}{\rm I}.$$ $$\,\,\,\,\,\,$$ $$p+m+c=13/20$$
$${\rm I}{\rm I}{\rm I}.$$ $$\,\,\,\,\,\,$$ $$\left( p \right) \times \left( m \right) \times \left( c \right) = 1/10$$
A
Only relation $${\rm I}$$ is true
B
Only relation $${\rm I}$$$${\rm I}$$ is true
C
Relations $${\rm I}$$$${\rm I}$$ and $${\rm I}$$$${\rm I}$$$${\rm I}$$ are true
D
Relations $${\rm I}$$ and $${\rm I}$$$${\rm I}$$$${\rm I}$$ are true
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