1
JEE Advanced 2016 Paper 2 Offline
+3
-0
Football teams $${T_1}$$ and $${T_2}$$ have to play two games against each other. It is assumed that the outcomes of the two games are independent. The probabilities of $${T_1}$$ winning, drawing and losing a game against $${T_2}$$ are $${1 \over 2},{1 \over 6}$$ and $${1 \over 3}$$ respectively. Each team gets $$3$$ points for a win, $$1$$ point for a draw and $$0$$ point for a loss in a game. Let $$X$$ and $$Y$$ denote the total points scored by teams $${T_1}$$ and $${T_2}$$ respectively after two games.

$$\,\,\,\,P\,\left( {X > Y} \right)$$ is

A
$${1 \over 4}$$
B
$${5 \over 12}$$
C
$${1 \over 2}$$
D
$${7 \over 12}$$
2
JEE Advanced 2016 Paper 2 Offline
+3
-0
Football teams $${T_1}$$ and $${T_2}$$ have to play two games against each other. It is assumed that the outcomes of the two games are independent. The probabilities of $${T_1}$$ winning, drawing and losing a game against $${T_2}$$ are $${1 \over 2},{1 \over 6}$$ and $${1 \over 3}$$ respectively. Each team gets $$3$$ points for a win, $$1$$ point for a draw and $$0$$ point for a loss in a game. Let $$X$$ and $$Y$$ denote the total points scored by teams $${T_1}$$ and $${T_2}$$ respectively after two games.

$$P\,\left( {X = Y} \right)$$ is

A
$${{11} \over {36}}$$
B
$${{1} \over {3}}$$
C
$${{13} \over {36}}$$
D
$${{1} \over {2}}$$
3
JEE Advanced 2016 Paper 1 Offline
+3
-1
A computer producing factory has only two plants $${T_1}$$ and $${T_2}.$$ Plant $${T_1}$$ produces $$20$$% and plant $${T_2}$$ produces $$80$$% of the total computers produced. $$7$$% of computers produced in the factory turn out to be defective. It is known that $$P$$ (computer turns out to be defective given that it is produced in plant $${T_1}$$)
$$= 10P$$ (computer turns out to be defective given that it is produced in plant $${T_2}$$),
where $$P(E)$$ denotes the probability of an event $$E$$. A computer produced in the factory is randomly selected and it does not turn out to be defective. Then the probability that it is produced in plant $${T_2}$$ is
A
$${{36} \over {73}}$$
B
$${{47} \over {79}}$$
C
$${{78} \over {93}}$$
D
$${{75} \over {83}}$$
4
JEE Advanced 2014 Paper 2 Offline
+4
-1
Three boys and two girls stand in a queue. The probability, that the number of boys ahead of every girl is at least one more than the number of girls ahead of her, is
A
$${1 \over 2}$$
B
$${1 \over 3}$$
C
$${2 \over 3}$$
D
$${3 \over 4}$$
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