1
IIT-JEE 2011 Paper 1 Offline
+4
-1

Let $${U_1}$$ and $${U_2}$$ be two urns such that $${U_1}$$ contains $$3$$ white and $$2$$ red balls, and $${U_2}$$ contains only $$1$$ white ball. A fair coin is tossed. If head appears then $$1$$ ball is drawn at random from $${U_1}$$ and put into $${U_2}$$. However, if tail appears then $$2$$ balls are drawn at random from $${U_1}$$ and put into $${U_2}$$. Now $$1$$ ball is drawn at random from $${U_2}$$ being white is

Given that the drawn ball from $${U_2}$$ is white, the probability that head appeared on the coin is

A
$${{17} \over {23}}$$
B
$${{11} \over {23}}$$
C
$${{15} \over {23}}$$
D
$${{12} \over {23}}$$
2
IIT-JEE 2010 Paper 1 Offline
+4
-1
Let $$\omega$$ be a complex cube root of unity with $$\omega \ne 1.$$ A fair die is thrown three times. If $${r_1},$$ $${r_2}$$ and $${r_3}$$ are the numbers obtained on the die, then the probability that $${\omega ^{{r_1}}} + {\omega ^{{r_2}}} + {\omega ^{{r_3}}} = 0$$ is
A
$${1 \over 18}$$
B
$${1 \over 9}$$
C
$${2 \over 9}$$
D
$${1 \over 36}$$
3
IIT-JEE 2010 Paper 2 Offline
+4
-1
A signal which can be green or red with probability $${4 \over 5}$$ and $${1 \over 5}$$ respectively, is received by station A and then transmitted to station $$B$$. The probability of each station receving the signal correctly is $${3 \over 4}$$. If the signal received at atation $$B$$ is green, then the probability that the original signal was green is
A
$${3 \over 5}$$
B
$${6 \over 7}$$
C
$${20 \over 23}$$
D
$${9 \over 20}$$
4
IIT-JEE 2009 Paper 1 Offline
+4
-1

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

The probability that X = 3 equals
A
$${{25} \over {216}}$$
B
$${{25} \over {36}}$$
C
$${{5} \over {36}}$$
D
$${{125} \over {216}}$$
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