Tough Decisions
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Have a Heart
A set of eight cards, consisting of seven spades and one heart are shuffled
and dealt face down to four piles of two cards each. You select one pile and
turn up a spade. Which method maximizes the probability of turning up the heart
on a second try?
A. Select another card from the same pile.
B. Select a card from a different pile.
C. Neither, both methods have the same probability.
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The Pool Also Rises
A canoe is floating in a pool. From outside the pool, you drop a brick
in the canoe and the water level in the pool rises as a result of your
action. If you were to miss the canoe and the brick fell in the water
the water level would also rise. Which way would the pool rise the most?
A. Brick in the canoe.
B. Brick in the water.
C. Neither, it would rise the same amount.
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Stirred, Not Shaken
A cocktail shaker is filled to the 4 oz. level with gin. A second cocktail shaker
is filled to the 4 oz. level with bourbon. A teaspoonful of the bourbon is taken from
the second shaker, put into the first shaker and stirred to mix it with the gin. Next
a teaspoonful of the mixture in the first shaker is transferred to the second shaker and
stirred to mix it with the bourbon. Now what is the present condition?
A. There is more bourbon in the first shaker than gin in the second shaker.
B. There is more gin in the second shaker than bourbon in the first shaker.
C. There is just as much bourbon in the first shaker as gin in the second shaker.
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Mr. Sandman
On day on the beach, just to keep from being bored, you fill two identical pails
with sand. One pail is filled with dry sand well away from the ocean and the other
is filled with wet sand where the tides come in.
Which pail is heavier?
A. The one with dry sand.
B. The one with wet sand.
C. Neither, they weigh the same.
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Pizza the Action
You have just answered the super bonus question at a quiz show.
You'll win 55 pepperoni pizzas if you can guess behind which of
three doors they are found.
You have a bad head cold today, so your sense of smell is no help.
You pick door number 1, but before you open it.
The host opens door number three to reveal no pizzas there.
The host than asks you if you would like to change your selection
to door number 2. You love pizza! Should you...
A. Change your selection to door number 2.
B. Stay with door number 1.
C. It doesn't matter, either selection offers the same probability.
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The Solutions follow.
I am interested to your solutions in the meantime, so please send EMail.
ANSWERS
:
go back to
questions.
- Have a Heart
- C. - This is a "warm-up", really. Seven cards remain after your selection one heart and six spades. The probability of any one of them being a heart is one chance in seven. Your prior card arrangement and selection does not effect the current situation.
- The Pool Also Rises
- A. - The brick in the canoe displaces a volume of water equivalent to its weight. The brick under water displaces its volume. Since a brick's weight of water takes more space than a brick's volume of water, the pool will rise more with the brick in the canoe.
- Stirred, Not Shaken
- C - There is the same amount of gin in the bourbon as bourbon in the gin. I am amazed at how people believe this problem is more complicated than it is.
After the transfers and mixing, the condition is as follows:
Shaker 1 has G ounces of gin + b ounces of bourbon, total 4 ounces.
Shaker 2 has B ounces of bourbon + g ounces of gin, total 4 ounces.
...but originally:
Shaker 1 had G ounces of gin + g ounces of gin, total 4 ounces
(i.e. the gin in shaker 1 now + the gin in shaker 2 now).
Shaker 2 had B ounces of bourbon + b ounces of bourbon, total 4 ounces
(i.e. the bourbon in shaker 2 now + the bourbon in shaker 1 now).
Since
G+b=4 and G+g=4, we must conclude b=g.
- Mr. Sandman
- A. - The pail with the dry sand contains more sand than the pail with the wet sand. Sand is heavier than water.
- Pizza the Action
- A. - This answer always gets arguments, but you double your winning chances by changing doors.
The host is actually offering you two doors in exchange for the one you have selected! If you keep door #1, you have 1 chance in three of being a winner. The host revealed one of the remaining doors that was NOT a winner (we must assume the host would not reveal the winning door, that wouldn't be any fun) and offers you the other one. Since there are two chances in three of the prize being behind one of TWO doors, the switch DOUBLES your chance of winning!