1
GATE ME 2015 Set 3
+2
-0.6
A coin is tossed thrice. Let $$X$$ be the event that head occurs in each of the first two tosses. Let $$Y$$ be the event that a tail occurs on the third toss. Let $$Z$$ be the event that two tails occur in three tosses. Based on the above information, which one of the following statements is TRUE?
A
$$X$$ and $$Y$$ are not independent
B
$$Y$$ and $$Z$$ are dependent
C
$$Y$$ and $$Z$$ are independent
D
$$X$$ and $$Z$$ are independent
2
GATE ME 2015 Set 2
+2
-0.6
The chance of a student passing an exam is $$20$$% The chance of a student passing the exam and getting above $$90$$% marks in it is $$5$$%. Given that a student passes the examination, the probability that the student gets above $$90$$% marks is
A
$${1 \over {18}}$$
B
$${1 \over {4}}$$
C
$${2 \over {9}}$$
D
$${5 \over {18}}$$
3
GATE ME 2014 Set 2
+2
-0.6
A box contains $$25$$ parts of which $$10$$ are defective. Two parts are being drawn simultaneously in a random manner from the box. The probability of both the parts being good is
A
$${7 \over {20}}$$
B
$${42 \over {125}}$$
C
$${25 \over {29}}$$
D
$${5 \over {9}}$$
4
GATE ME 2014 Set 2
Numerical
+2
-0
Consider an unbiased cubic die with opposite faces coloured identically and each face coloured red, blue or green such that each color appears only two times on the die. If the die is thrown thrice, the probability of obtaining red colour on top face of the die at least twice is ________.