In a test of a printed circuit board using a random test pat

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.

What is the probability that exactly five bits are 1s and five bits are 0s?

Solution

the probability that exactly five bits are 1s and five bits are 0s is 10C5 X (1/2)⁵ X (1/2)⁵ = 252 / 1024 = 0.246