Biased Coin

A biased coin with the probability of getting a head is 70% of the time and tail 30%. That is, P(H) = 0.7 and P(T) = 0.3. Toss the coin THREE times. Find the following probabilities: P(HHT) and P(2 Heads).

First notice that the two probabilities are not the same. P(HHT) asks for the probability of getting a sequence of HHT, while P(2 Heads) asks for the probability of getting exactly 2 heads. There are 3 ways to get exactly 2 heads in 3 tosses: HHT, HTH, and THH. Also, note that the two events (whether we get a H or a T) are independent.

P(HHT) = P(H)P(H)P(T) = (.7)(.7)(.3) = .147.
P(2Hs) = P(HHT) + P(HTH) + P(THH) = .147 + .147 + .147 = .441