One in five of Cadbury's specially marked chocolate bars (Promotion Products) will be packaged in a wrapper that entitles the holder to an instant win prize. Each instant win prize is a Cadbury chocolate bar of the winner's choice.

Assume that the number of “Promotion Products” produced is massive (in fact, hugely in excess of the anticipated sales during the “Promotion Period”).
Cadbury will award a total of 2,263,400 prizes, ie, there will be 2,263,400 Winning Wrappers.
All calculated probabilities must be correct to 4 decimal places.
Show how you obtain your answers.
(a) (i) Tabulate (to 4 decimal places) the probability that a customer will win if she buys
1 of Cadbury’s specially marked chocolate bars.
2 of Cadbury’s specially marked chocolate bars.
etc, etc, etc (ie, for 3, 4, ..,18 specially marked chocolate bars).
19 of Cadbury’s specially marked chocolate bars.
20 of Cadbury’s specially marked chocolate bars.

Explain how you obtain your probabilities. In your explanation, include reference to any assumptions you have made.
(ii) How many specially marked chocolate bars must a person buy to be certain of winning? Explain your answer.

The probability of winning is 1/5 = 0.2? or it is the probability to win given 1 package is bought? I'm confused.

Obviously part a) is asking you to tabulate the probability mass functions by software like excel/R etc. If the question here specify a finite number of chocolate bars then theoretically speaking you should consider the hypergeometric distribution; But when the total number is large, it can be closely approximated by Binomial distribution as well.

If its binomial distribution and my above calculation is correct.. I have further question that

How many specially marked chocolate bars do you expect that Cadbury must sell before all prizes are won? Discuss.
Assume that every holder of a winning wrapper claims the prize.

Is that E(X) = 2,263,400 x 0.2 = 452,680?

Last edited by lemon_kaka; 08-28-2013 at 01:47 AM.