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. p/16
• B. p¹⁶
• C. ¹⁶C₁p¹⁶
• D. 1-(1-p)¹⁶

Answer 1

Answer: (D)

1-(1-p)¹⁶

Answer 2

Probability of correct bit appearing is (1 – p).

∴ Probability of correct number = (1 – p)¹⁶ and

Hence probability of incorrect number

= 1 = (1 – p)¹⁶.