Question

A binary number is made up of $16$ bits. The probability of an incorrect bit appearing is $p$ and the errors in different bits are independent of one another. The probability of forming an incorrect number is.

• A. $\frac{p}{16}$
• B. $p^{16}$
• C. ${}^{16}C_1{p}^{16}$
• D. $1-{(1-p)}^{16}$

Answer 1

The correct option is D

$1-{(1-p)}^{16}$

Explanation for the correct otpion:

Finding the probability:

It is given in the question that, the probability of an incorrect bit is $p$

Hence, the probability of a correct bit appearing is $1-p$

The probability of getting a correct binary number is ${(1-p)}^{16}$

Hence, the probability of getting an incorrect number is $1-{(1-p)}^{16}$

Hence, the correct answer is option (D).