Marketing A company includes instant-win tickets with $10,000,000$ of its products. Of the prizes offered, one is a large cash prize, $1,600,000$ are small cash prizes, and the other prizes are free samples of the company's products.
a. Find the theoretical probability of winning each type of prize.
b. Design and conduct a simulation to determine the prizes for 100 products.
c. Find the experimental probability for winning each type of prize.