### Probability, Random Variables and Density Functions

1. A coin is biased so that a head is three times as likely to occur as a tail. Find the expected number of tails when this coin is tossed twice. 2. An attendant at a car wash is paid according to the number of cars that pass through. Suppose the probabilities are 1/12, 1/12, ¼, ¼, 1/6, and 1/6, respectively, that the a