Question

5. Now suppose that there are two sizes of soda, 1-litre bottles (for $00/bottle) and 2-litre bottles (for $1.50/bottle). Again some bottles of both sizes are “special” in that the cap might contain a bonus. A special 1-litre bottle has a red cap and a special 2-litre bottle has a purple cap.

Suppose a red cap will give you

• Nothing with a probability 1/5
• A free regular 2-litre bottle with a probability 1/5
• A free special 1-litre bottle with a probability 2/5 (red cap)
• A free special 2-litre bottle with a probability 1/5 (purple cap)

And a purple cap will give you

• Nothing with a probability 1/5
• A free regular 2-litre bottle with a probability 1/5
• A free special 1-litre bottle with a probability 1/5 (red cap)
• A free special 2-litre bottle with a probability 2/5 (purple cap)

(a) How much are you effectively paying per litre for soda if you buy

A special 1-litre bottle?

A special 2-litre bottle?

(b) Suppose you are not so interested in the soda but want to collect coloured caps. How many coloured caps (red or purple) will you get, on average, with the purchase of:

A special 1-litre bottle?

A special 2-litre bottle?

Answer 1