Below is an XQR table for 0 7 Suppose that a 0 1 7 is an u

Below is an XQR table for 0, ..., 7 Suppose that a {0, 1, ..., 7} is an unknown value that you are trying to guess. Suppose that the probability that a is equal to i, i = 0, ..., 7, is each 1/8. Suppose that the probability that b is equal to i, i = 0, ..., 7, is also each 1/8. You are given the value of a b and nothing else. What is the probability of guessing the value of a correctly in one try?

Solution

We know that a has 8 numbers in its sample space of guessing and the probability is 1/8.

In the table of XOR, k=a XOR b ,where k= 0,1,....7 and each value repeated 8 times over the 64 values of table.

After knowing the value of a XOR b , we have 8 values in sample space. It may be any number from 0 to 7.

Therefore the probability of guessing the value of a correctly in one try is 1/8.