ONE MORE STEP TOWARD BETTER TOMMOROW
Thursday, 7 August 2014
A pair of dice is rolled until a sum of either
is obtained. Find the probability that
A sum of
can be obtained in
from a total number of
ways of throwing a pair of dice. If we let
denote the event
of obtaining a sum of
, we have
Similarly, let the event
be that of obtaining a sum of
; this can happen in
Finally, if we let
be the event of obtaining neither a
, we have
Now, we want a sum of
to come before a sum of
. Think about how this can happen. Every time you roll the pair of dice, you should either get a sum of
or you should get neither a sum of
Therefore, the following (mutually exclusive) sequences of throws leads us to a sum of
before a sum of
The required probability is obtained by adding the terms in the right column.
In passing, note that the probability of obtaining a
Can you appreciate why obtaining a
is more likely than obtaining a
Two unit squares are chosen at random from a standard chessboard. What is the probability that the two squares have exactly one corner in common?
The total number of ways of selecting two squares from a standard chessboard is simply
Now, let us find the number of ways of selecting a pair with exactly one corner in common. For that, consider the following figure.
It is immediately evident that the number of favorable ways is
The required probability is
August 07, 2014
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