Four fair dice
and
each having six faces numbered 1, 2, 3, 4, 5 and 6 are rolled, simultaneously. The probability that
shows a number appearing on one of
and
is
, then
is
Text Solution
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Sample space 
Favourable events
Case I or Case II or Case III
Case I First, we should select one number for
which appears on all i.e.
.
Case II For
there are
ways. Now, it appears on any one of
i.e.
.
For other two there are
ways

Case III For
there are
ways. Now, it appears on any two of 

For other one there are 5 ways.

Required probability

and 
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