The numbers on the dice for which the sum of the numbers
can be 6 is: (1,5) , (2, 4), (3,3) , (4,2), (5,1).
Now we
need to get one event out of six possible events. So the probability of getting any
particular number when a die is tossed is 1/6.
Also, the
probability of two events occurring simultaneously is the product of the probabilities
of their occurring individually.
Therefore the probability
of each of the five cases we have to consider occuring
is:
The first die has 1 and the second 5: the probability
is 1/6 * 1/6 = 1/36
The first die has 2 and the second 4:
the probability is 1/6 * 1/6 = 1/36
The first die has 3 and
the second 3: the probability is 1/6 * 1/6 = 1/36
The first
die has 4 and the second 2: the probability is 1/6 * 1/6 =
1/36
The first die has 5 and the second 1: the probability
is 1/6 * 1/6 = 1/36
To get the sum as 6 any of these cases
will do. So the probability that we get a 6 is the sum of the individual probabilities
we just derived, which is equal to 5*(1/36)=
5/36.
Therefore the probability that we get
the sum as 6 when two dice are thrown is 5/36.
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