1
JEE Advanced 2013 Paper 1 Offline
+4
-1
Four persons independently solve a certain problem correctly with probabilities $${1 \over 2},{3 \over 4},{1 \over 4},{1 \over 8}.$$ Then the probability that the problem is solved correctly by at least one of them is
A
$${{235} \over {256}}$$
B
$${{21} \over {256}}$$
C
$${{3} \over {256}}$$
D
$${{253} \over {256}}$$
2
IIT-JEE 2012 Paper 2 Offline
+4
-1
Four fair dice $${D_1,}$$ $${D_2,}$$ $${D_3}$$ and $${D_4}$$ ; each having six faces numbered $$1, 2, 3, 4, 5$$ and $$6$$ are rolled simultaneously. The probability that $${D_4}$$ shows a number appearing on one of $${D_1},$$ $${D_2}$$ and $${D_3}$$ is
A
$${{91} \over {216}}$$
B
$${{108} \over {216}}$$
C
$${{125} \over {216}}$$
D
$${{127} \over {216}}$$
3
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

The probability of the drawn ball from $${U_2}$$ being white is

A
$${{13} \over {30}}$$
B
$${{23} \over {30}}$$
C
$${{19} \over {30}}$$
D
$${{11} \over {30}}$$
4
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
$${{12} \over {23}}$$
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