Math Problem Statement

In a test of a printed circuit board using a random test pattern, an array of 10 bits is

equally likely to be 0 or 1. Assume the bits are independent.

(a) What is the probability that all bits are 1s?

(b) What is the probability that all bits are 0s?

(c) What is the probability that exactly 5 bits are 1s and 5 bits are 0s?

Solution

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Math Problem Analysis

Mathematical Concepts

Probability
Binomial Distribution

Formulas

P(bit = 1) = 1/2
P(bit = 0) = 1/2
P(X = k) = C(n, k) * p^k * (1-p)^(n-k)

Theorems

Binomial Theorem

Suitable Grade Level

Grades 10-12