In a random pattern of eight bits used to test a micro-circuit, each bit is equally likely to be 0 or 1. Assume the values of the bits are independent.
a. What is the probability that all eight bits are 1?
b. What is the probability that exactly three of the bits are 1?
c. What is the probability that at least six of the bits are 1?
d. What is the probability that least two of the bits are 1?