Coins, Births, and Other Random Events
Examples
of random events such as tossing coins are used in all books on
probability. But is flipping a coin
really a random event?
Tossing
coins dates back to ancient Roman times when the coins usually consisted of the
Emperor’s head on one side (i.e., heads) and another icon such as a ship on the
other side (i.e. ships). Tossing coins
was used in both fortune telling and ancient Roman games.
A
Chinese form of divination called the I-Ching
(pronounced as E-Ching) is thought to be at least 4000 years old. It consists of 64 hexagrams made up of six
horizontal lines. Each line is either
broken or unbroken, representing the yin and yang. These 64 hexagrams are supposed to represent
all possible situations in life. To
consult the I-Ching, a question is asked and the three coins are tossed six
times. The way the coins fall, either
heads up or heads down, determines whether the line is broken 9yin) or unbroken
(yang). Once the hexagon is determined,
its meaning is consulted and interpreted to get the answer the question. (Note:
Another method is used to determine the hexagon employs yarrow sticks.)
In the
16th century, a mathematician named Abraham Demoivre used the
outcomes of tossing coins to study what later became known as the normal
distribution; however, his work at that time was not widely known.
Mathematicians
usually consider the outcomes of a coin as a random event. That is, each probability of getting a head
is 1/2 and the probability of getting a tail is 1/2. Also, it is not
possible to predict with 100% certainty which outcome will occur. But new studies question this theory. During World War II a South African mathematician
named John Kerrich tossed a coin 10,000 times while he was interned in a German
prison camp. Unfortunately, the results
of his experiment were never recorded, so we don’t know the number of heads
that occurred.
Several
studies have shown that when a coin-tossing device is used, the probability
that a coin will land on the same side on which it is placed on the
coin-tossing device is about 51%. It
would take about 10,000 tosses to become aware of this bias. Furthermore, researchers showed that when a
coin is spun on its edge, the coin would fall tails up about 80% of the time
since there is more metal on the heads side of the coin. This makes the coin slightly heavier on the
heads side than on the tails side.
Another
assumption commonly made in probability theory is that the number of male
births is equal to the number of female births and that the probability of a
boy being born is 1/2 and the probability of a girl being born is 1/2. We know that this is not exactly true.
In
the later 1700s, a French mathematician named Pierre Simon Laplace attempted to
prove that more males than females are born.
He used records from 1745 to 1770 in Paris and showed that the
percentage of females born was about 49%.
Although these percentages vary somewhat from location to location,
further surveys show they are generally true worldwide. Even though there are discrepancies, we
generally consider the outcomes to be 50-50 since these discrepancies is
relatively small.
Based
on this article, would you consider the coin tossing at the beginning of a
football game fair?
by: Marie Louissie Ynez U. Lavega
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