Let's denote the random numbers generated by A and B as
a and
b respectively. Given that the sum of the two numbers is 12 , we have the equation:
a+b=12We want to find the probability that
a and
b are equal under this condition.
First, let's list out the set of possible single-digit values from which
a and
b can be generated, which are
{1,2,3,4,5,6,7,8}. Given the equation
a+b=12, we can find the pairs
(a,b) that satisfy this condition:
‌(a=4,b=8)‌(a=5,b=7)‌(a=6,b=6)‌(a=7,b=5)‌(a=8,b=4) As seen above, there are exactly five pairs that satisfy the condition
a+b=12.
Next, we need to determine how many of these pairs have equal numbers. The only pair where the numbers are equal is
(6,6).
Therefore, there is only one favorable outcome out of the five possible outcomes where
a and
b are equal.
Thus, the probability that the two numbers are equal given that their sum is 12 is:
Hence, the correct answer is:
Option B:
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