Question:
A soft drink manufacturer is using a "winning" cap as a sales promotion. The purchaser can get a prize if they buy a bottle that has a "Winner" symbol under the cap. Winning symbol caps are placed randomly on 5% of the bottles.
You buy a six-pack of the soft drink.
a) State the exact probability distribution that applies to this circumstance.
b) What is the probability that you win something? Give clear notation of the probability calculated.
c) What is the Poisson approximation to this distribution? Estimate the probability that you win something using this approximation.
d) Comment on the results of the two calculations.