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The data string of length is 4 bytes.

The number of possible two strings is S₁ and S₂.

The probability that S₁ and S₂differ in any one of the bytes is 0.5.

The characteristics of the Binomial experiment are as follows:

• The experiments consist of n trials
• Each trial consists of two outcomes only, either success or failure.
• The probability of success is represented as 鈥減鈥�, and the probability of failure is defined as 鈥渜鈥�.

The trials are independent to each other.

The data string of length is 4 bytes. So, the number of trials is n=4.

The two possible outcomes are:

• Success, S= the string that matches with the byte.
• Failure, F= the line does not match with the byte.

For each trial,

The probability of success is,

$$\begin{gathered} p=P\left(S\right) \\ =0.5 \end{gathered}$$

The probability of failure is,

$$\begin{gathered} q=1-p \\ =1-0.5 \\ =0.5 \end{gathered}$$

The probability of success is the same for all the trials.

Here, the trials are closely independent because one byte does not affect the matching of the other bytes.

The random variable x is a data string of the length of 4 bytes or trials.

Hence, the x is approximately a binomial random variable,and the x follows a binomial distribution with n=4 and p=0.5.

i.e;$x~B\left(4,0.5\right)$