1
GATE CSE 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
2
GATE CSE 2015 Set 3
Numerical
+2
-0
Suppose $${X_i}$$ for $$i=1,2,3$$ are independent and identically distributed random variables whose probability mass functions are $$\,\,\Pr \left[ {{X_i} = 0} \right] = \Pr \left[ {{X_i} = 1} \right] = 1/2\,\,$$ for $$i=1,2,3.$$ Define another random variable $$\,\,Y = {X_1}{X_2} \oplus {X_3},\,\,$$ where $$\oplus$$ denotes $$XOR.$$ Then $$\Pr \left[ {Y = 0\left| {{X_3} = 0} \right.} \right]$$ =________.
3
GATE CSE 2014 Set 1
Numerical
+2
-0
Four fair six-sided dice are rolled. The probability that the sum of the results being 22 is X/1296. The value of X is__________
4
GATE CSE 2014 Set 3
Numerical
+2
-0
Let S be a sample space and two mutually exclusive events A and B be such that $$A\, \cup \,B = \,S$$. If P(.) denotes the probability of the event, the maximum value of P(A) P(B) is ________________.