1
IIT-JEE 2009 Paper 1 Offline
+3
-1

A fair die is tossed repeatedly until a six is obtained. Let X denote the number of tosses required.

The conditional probability that $$X\ge6$$ given $$X>3$$ equals :

A
$${{125} \over {216}}$$
B
$${{25} \over {216}}$$
C
$${{5} \over {36}}$$
D
$${{25} \over {36}}$$
2
IIT-JEE 2008 Paper 2 Offline
+3
-1

An experiment has 10 equally likely outcomes. Let A and B be two non-empty events of the experiment. If A consists of 4 outcomes, the number of outcomes that B must have so that A and B are independent is :

A
2, 4 or 8
B
3, 6 or 9
C
4 or 8
D
5 or 10
3
IIT-JEE 2008 Paper 1 Offline
+3
-1
Consider the system of equations $$ax+by=0; cx+dy=0,$$
where $$a,b,c,d$$ $$\in \left\{ {0,1} \right\}$$

STATEMENT - 1 : The probability that the system of equations has a unique solution is $${3 \over 8}.$$ and

STATEMENT - 2 : The probability that the system of equations has a solution is $$1.$$
A
STATEMENT - 1 is True, STATEMENT - 2 is True; STATEMENT - 2 is a correct explanation for STATEMENT - 1
B
STATEMENT - 1 is True, STATEMENT - 2 is True; STATEMENT - 2 is NOT a correct explanation for STATEMENT - 1
C
STATEMENT - 1 is True, STATEMENT - 2 is False.
D
STATEMENT - 1 is False, STATEMENT - 2 is True.
4
IIT-JEE 2007
+3
-0.75
One Indian and four American men and their wives are to be seated randomly around a circular table. Then the conditional probability that the Indian man is seated adjacent to his wife given that each American man is seated adjacent to his wife is
A
$${1 \over 2}$$
B
$${1 \over 3}$$
C
$${2 \over 5}$$
D
$${1 \over 5}$$
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