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Smokey's Smokes (Posted on 2010-06-03) Difficulty: 1 of 5
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?

No Solution Yet Submitted by John zadeh    
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Solution solution | Comment 2 of 6 |
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

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