A store sells three brands of cigarettes: $3.15 Star lights, $4.30 Vegas slims, and $5.20 Royal 100's. (Tax included) A man named Smokey walks into the store, and buys 2 packs of cigarettes, one pack for himself and the other pack for a friend. He hands the cashier a $20 note, and is returned a few bills and 3 coins in change (exclude dollars or half dollars). What's the probability, that the man smokes Royal 100's?

In order for exact change to include only three coins of US currency, Smokey must have purchased either:

1. One pack of Star lights and one pack of Vegas slims
   purchase: $ 7.45
   change: $12.55
   coins: 55 cents = two quarters and one nickle
   
2. Two packs of Vegas slims
   purchase: $ 8.60
   change : $11.40
   coins: 40 cents = one quarter, one dime and one nickle
    
3. Two packs of Royal 100's
   purchase: $10.40
   change: $ 9.60
   coins: 60 cents = two quarters and one dime

There is then a 1/3 probability Smokey smokes Royal 100's.

Without half dollar or dollar coins, the change from the other possible purchases can not be given as three coins of US currency:

• two packs of Star lights
  purchase: $ 6.30
  change: $13.70 (70 cents)
  
• one pack each, Star lights and Royal 100's
  purchase: $ 8.35
  change: $11.65 (65 cents)
  
• one pack each, Vegas slim and Royal 100's
  purchase: $ 9.50
  change: $10.50 (50 cents)

Edited on June 3, 2010, 12:43 pm

Posted by Dej Mar on 2010-06-03 12:39:26