EXERCISE

12.3.6:Calculating probabilities of independent events.

A biased coin is flipped 10 times. In a single flip of the coin, the probability of heads is 1/3 and the probability of tails is 2/3. The outcomes of the coin flips are mutually independent. What is the probability of each event?

(a)

Every flip comes up heads.

(b)

The first 5 rolls come up heads. The last 5 flips come up tails.

(c)

The first roll comes up heads. The rest of the rolls come up tails.