1
JEE Advanced 2013 Paper 2 Offline
+4
-1
A box $${B_1}$$ contains $$1$$ white ball, $$3$$ red balls and $$2$$ black balls. Another box $${B_2}$$ contains $$2$$ white balls, $$3$$ red balls and $$4$$ black balls. A third box $${B_3}$$ contains $$3$$ white balls, $$4$$ red balls and $$5$$ black balls.

If $$2$$ balls are drawn (without replacement) from a randomly selected box and one of the balls is white and the other ball is red, the probability that these $$2$$ balls are drawn from box $${B_2}$$ is

A
$${{116} \over {181}}$$
B
$${{126} \over {181}}$$
C
$${{65} \over {181}}$$
D
$${{55} \over {181}}$$
2
JEE Advanced 2013 Paper 2 Offline
+4
-1
A box $${B_1}$$ contains $$1$$ white ball, $$3$$ red balls and $$2$$ black balls. Another box $${B_2}$$ contains $$2$$ white balls, $$3$$ red balls and $$4$$ black balls. A third box $${B_3}$$ contains $$3$$ white balls, $$4$$ red balls and $$5$$ black balls.

If $$1$$ ball is drawn from each of the boxex $${B_1},$$ $${B_2}$$ and $${B_3},$$ the probability that all $$3$$ drawn balls are of the same colour is

A
$${{82} \over {648}}$$
B
$${{90} \over {648}}$$
C
$${{558} \over {648}}$$
D
$${{566} \over {648}}$$
3
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
$${{253} \over {256}}$$
4
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
$${{127} \over {216}}$$
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