1
IIT-JEE 2007 Paper 2 Offline
+3
-1
Let $${E^c}$$ denote the complement of an event $$E.$$ Let $$E, F, G$$ be pairwise independent events with $$P\left( G \right) > 0$$ and $$P\left( {E \cap F \cap G} \right) = 0.$$ Then $$P\left( {{E^c} \cap {F^c}|G} \right)$$ equals
A
$$P\left( {{E^c}} \right) + P\left( {{F^c}} \right)$$
B
$$P\left( {{E^c}} \right) - P\left( {{F^c}} \right)$$
C
$$P\left( {{E^c}} \right) - P\left( F \right)$$
D
$$P\left( E \right) - P\left( {{F^c}} \right)$$
2
IIT-JEE 2006
+5
-1.25
There are $$n$$ urns, each of these contain $$n+1$$ balls. The ith urn contains $$i$$ white balls and $$(n+1-i)$$ red balls. Let $${u_i}$$ be the event of selecting ith urn, $$i=1,2,3........,n$$ and $$w$$ the event of getting a white ball.

If $$P\left( {{u_i}} \right) \propto i,\,$$ where $$i=1,2,3,.......,n,$$ then $$\mathop {\lim }\limits_{n \to \infty } P\left( w \right) =$$

A
$$1$$
B
$$2/3$$
C
$$3/4$$
D
$$1/4$$
3
IIT-JEE 2006
+5
-1.25
There are $$n$$ urns, each of these contain $$n+1$$ balls. The ith urn contains $$i$$ white balls and $$(n+1-i)$$ red balls. Let $${u_i}$$ be the event of selecting ith urn, $$i=1,2,3........,n$$ and $$w$$ the event of getting a white ball.

If $$P\left( {{u_i}} \right) = c,$$ (a constant) then $$P\left( {{u_n}/w} \right) =$$

A
$${2 \over {n + 1}}$$
B
$${1 \over {n + 1}}$$
C
$${n \over {n + 1}}$$
D
$${1 \over 2}$$
4
IIT-JEE 2006
+5
-1.25
There are $$n$$ urns, each of these contain $$n+1$$ balls. The ith urn contains $$i$$ white balls and $$(n+1-i)$$ red balls. Let $${u_i}$$ be the event of selecting ith urn, $$i=1,2,3........,n$$ and $$w$$ the event of getting a white ball.

Let $$P\left( {{u_i}} \right) = {1 \over n},$$ if $$n$$ is even and $$E$$ denotes the event of choosing even numbered urn, then the value of $$P\left( {w/E} \right)$$ is

A
$${{n + 2} \over {2n + 1}}$$
B
$${{n + 2} \over {2\left( {n + 1} \right)}}$$
C
$${n \over {n + 1}}$$
D
$${1 \over {n + 1}}$$
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