Question

In a test of a printed circuit board using a random test pattern, an array of 14 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).

Answer 1

The probability that all 14 bits are 1s = 0.000061

Explanation:

Probability that a bit is 1 is p = 0.5

Probability that a bit isn't 1 is q = 1 - 0.5 = 0.5

This is a binomial distribution problem

Binomial distribution function is represented by

P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

n = total number of sample spaces = 14

x = Number of successes required = 14

p = probability of success = 0.5

q = probability of failure = 0.5

P(X = 14) = ¹⁴C₁₄ (0.5)¹⁴ (0.5)¹⁴⁻¹⁴

P(X = 14) = ¹⁴C₁₄ (0.5)¹⁴ (0.5)⁰

P(X = 14) = 1 (0.000061)(1) = 0.000061