4. Suppose soda is sold in l-litre bottles. A promotion is announced and some bottles are "special" and have a red cap which might contain a bonus (on the underside of the cap ). To be precise , a red cap will give you I nothing with probability 1/3 a a free regular bottle with probability 1/3 I a free special bottle with probability 1/3 (a) If you buy a special bottle for $1.00, how much on average are you effectively paying per litre for soda ? (b) Suppose you are not so interested in the soda but want to collect red caps. How many red caps will you get, on average, with the purchase of one special bottle. [Counting of course the red cap you get with your purchase.] 5. Now suppose that there are two sizes of soda , 1-litre bottles (for $1.00 /bottle )and 2-]jtre bottles (for $1.50 /bottle ). Again some bottles of both sizes are "special" in that the cap might contain a bonus. A special 1-].itre bottle has a red cap and a special 2-litre bottle has a purple cap . Suppose a red cap will give you c nothing with probability 1/5 I a free regular 1-1itre bottle with probability 1/5 I a free special 1-litre bottle with probability 2/5 (red cap) I a free special 2-litre bottle with probability 1/5 (purple cap) and a purple cap will give you I nothing with probability 1/5 I a free regular 2-1itre bottle with prob ability 1/5 I a free special 1-litre bottle with probability 1/5 (red cap) o a free special Z-litre bottle with 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