Pokemon Probability Problem #2 ­ Raindance

Hiya!  It’s Master 1080 again.  This time I have
another probability problem.  This one won’t be as
confusing and difficult as Pokemon Probability Problem
#1 posted on Pojo on June 13, 2001 (Many thanks the
Pojo crew for actually posting it).  Here’s another
problem that I think everyone could try.  A scientific
calculator and knowledge of combinations will help.

Here’s the problem:

Your Blastiose is your Active Pokemon and it is facing
a Charizard (120 HP) with 20 damage on it.  Your
Blastoise has no Energy Cards attached to it and if
you end your turn, Charizard can finish your Blastoise
off for sure, especially since it will be charged up
on your opponent’s next turn.  Moreover, each person
is down to his or her last Pokemon, so it is crucial
that Charizard is knocked out.  It is your turn and
you just drew a Bill.  In your hand you now have a
total of 10 cards, 3 of which are Water Energy Cards,
1 of which is a Bill, and the rest of your hand (6
cards) are useless Trainers).  Also, both of you have
2 prizes left.

>From a previous Energy Search, you found out that only
3 Water Energies are left in your deck.  You deck now
consists of 10 cards, and you know that there are 3
Water Energies and 1 Bill in your deck.  You use your
Bill and hope to draw enough water Energy to Raindance
and knock out your opponent’s Charizard.  This means
that out of the 3 Water Energy in your deck, you have
to get at least one from your deck, or hope you get
that Bill to increase your chances some more.

What is the probability that you’ll win the game this
turn?

Here are the numbers for those of you who need to see
it:

Hand ­ 10 cards: 3 Water Energies, 1 Bill, 6 Useless
Trainers
Deck ­ 10 cards: 3 Water Energies, 1 Bill, 6 Other
cards
Discard ­ 35 Cards
Prizes ­ 2
Active ­ 3 cards: Blastoise (evolved from Wartortle
and Squirtle)
Bench ­ No Bench Pokemon

Requests for answers and responses about this
problem/article and how I wasted my time to Master
1080 at the_master1080@yahoo.com/

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