Calculate binomial probabilities and the expected value of a repeated coin game.

The probability of obtaining heads on a biased coin is \(\frac13\).

1. Sammy tosses the coin three times. Find the probability of getting[5]
   1. three heads;
   2. two heads and one tail.
2. Amir plays a game in which he tosses the coin 12 times.[5]
   1. Find the expected number of heads.

   2. Amir wins \( \$10\) for each head obtained, and loses \( \$ 6\) for each tail. Find his expected winnings.