Question

In a test of a printed circuit board using a random test pattern, an array of 16 bits is equally likely to be 0 or 1. Assume the bits are independent.

(a) What is the probability that all bits are 1s? Round your answer to six decimal places (e.g. 98.765432).
(b) What is the probability that all bits are 0s? Round your answer to six decimal places (e.g. 98.765432).
(c) What is the probability that exactly 8 bits are 1s and 8 bits are 0s? Round your answer to three decimal places (e.g. 98.765).

Answer 1

A) b) and c) answer has been explained below.

Explanation:

For the question would use 1's and 0's and taking probabilities to be equal for both using random test pattern whose formula is when p = q

then Simplify to

P[k] = nCk /2^n

A.Probability that all bits are 1s

16c16/2^16 = 1/65536

B. Probability that all bits are 0s

16c0/2^16 = 1/65536

C.the probability that exactly 8 bits are 1s and 8 bits are 0s

16c8/2^16 = 12870/65536 =>0.1963 ≈ 19.63%