1
AIEEE 2012
+4
-1
Three numbers are chosen at random without replacement from $$\left\{ {1,2,3,..8} \right\}.$$ The probability that their minimum is $$3,$$ given that their maximum is $$6,$$ is :
A
$${3 \over 8}$$
B
$${1 \over 5}$$
C
$${1 \over 4}$$
D
$${2 \over 5}$$
2
AIEEE 2011
+4
-1
Consider $$5$$ independent Bernoulli's trials each with probability of success $$p.$$ If the probability of at least one failure is greater than or equal to $${{31} \over 32},$$ then $$p$$ lies in the interval
A
$$\left( {{3 \over 4},{{11} \over {12}}} \right]$$
B
$$\left[ {0,{1 \over 2}} \right]$$
C
$$\left( {{11 \over 12},1} \right]$$
D
$$\left( {{1 \over 2},{{3} \over {4}}} \right]$$
3
AIEEE 2011
+4
-1
If $$C$$ and $$D$$ are two events such that $$C \subset D$$ and $$P\left( D \right) \ne 0,$$ then the correct statement among the following is
A
$$P\left( {{C \over D}} \right)$$$$\ge P\left( C \right)$$
B
$$P\left( {{C \over D}} \right)$$$$< P\left( C \right)$$
C
$$P\left( {{C \over D}} \right)$$$$= {{P\left( D \right)} \over {P\left( C \right)}}$$
D
$$P\left( {{C \over D}} \right)$$$$= P\left( C \right)$$
4
AIEEE 2010
+4
-1
Four numbers are chosen at random (without replacement) from the set $$\left\{ {1,2,3,....20} \right\}.$$

Statement - 1: The probability that the chosen numbers when arranged in some order will form an AP is $${1 \over {85}}.$$

Statement - 2: If the four chosen numbers form an AP, then the set of all possible values of common difference is $$\left( { \pm 1, \pm 2, \pm 3, \pm 4, \pm 5} \right).$$

A
Statement - 1 is true, Statement - 2 is true; Statement - 2 is not a correct explanation for Statement - 1.
B
Statement - 1 is true, Statement - 2 is false.
C
Statement - 1 is false, Statement -2 is true.
D
Statement - 1 is true, Statement - 2 is true; Statement - 2 is a correct explanation for Statement - 1.
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