1
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
$$\left( {{1 \over 2},{{3} \over {4}}} \right]$$
2
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
$$P\left( {{C \over D}} \right)$$$$= P\left( C \right)$$
3
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.
4
AIEEE 2010
+4
-1
An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colours is
A
$${2 \over 7}$$
B
$${1 \over 21}$$
C
$${1 \over 23}$$
D
$${1 \over 3}$$
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