Question: When dropped on a hard surface a thumbtack lands with its sharp point touching the surface with probability 2/3; it lands with its sharp point directed up into the air with probability 1/3. The tack is dropped and its landing position observed 15 times.
a. Find the probability that it lands with its point in the air at least 7 times.
b. If the experiment of dropping the tack 15 times is done repeatedly, what is the average number of times it lands with its point in the air?