As can easily be verified by means of the formula for the binomial distribution (or by listing all 16 possibilities), the probabilities of getting \(0,1,2,3\), or 4 red cards in four draws from a fair deck of cards are

\[\frac{1}{16} \quad \frac{4}{16} \quad \frac{6}{16} \quad \frac{4}{16} \quad \frac{1}{16}\]

Find the mean of this probability distribution using

(a) the formula that defines \(\mu\);

(b) the specific formula for the mean of a binomial distribution.