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
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