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

Question

3 months ago

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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).

Mathematics

1 answer:

AnnZ [12.3K] · Answer 1 · 2026-03-04T01:06:49+03:00

Answer:

A), B), and C) are clarified below.

Step-by-step explanation:

The inquiry involves using binary digits, employing probabilities that are equal for both conditions, by applying a random test pattern, where the formula is derived from p = q.

Simplifying gives us

P[k] = nCk / 2^n

A. Probability of all bits being 1s

16c16/2^16 = 1/65536

B. Probability of all bits being 0s

16c0/2^16 = 1/65536

C. The probability of having exactly 8 bits as 1s and the other 8 as 0s

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