Using a 52-card deck as an example, the odds of drawing a king from the deck are
1 in 12—or 4:(52 4) 4:48, which equals 1:12.
What is the difference between probabilityand odds?
Probability is usually expressed as a fraction (sometimes as a percentage). For exam-
ple, if there are ten pieces of fruit in a jar—three apples and seven oranges—then the
probability of taking out an orange is 7/10 (or seven chances of an orange out of a total
of ten chances). 429
RECREATIONAL MATH
Why is it difficult to win a lottery?
A
ccording to one state lottery site, a lottery “is a plan that provides for the dis-
tribution of money, property, or other reward or benefit to persons selected
by chance from among participants some or all of whom have given a considera-
tion for the chance of being selected.” In other words, a person buys a chance at
winning a certain sum of money. But in reality—as with many games of
chance—the game is not in the participant’s favor. With most lotteries, such as a
“lotto-type” lottery, a person has a better chance of being in a car or plane acci-
dent—or even being hit by lightning—than winning. But that doesn’t stop many
people. One recent statistic shows that, in the United States, an average of more
than $96 million is spent on lotteries every day, or more than $35 billion per year.
The reason for this “dream of winning” is simple: It’s how this game of
chance is perceived. Many people believe that if they just keep the same number,
it will eventually be chosen. What they often don’t understand when playing a
lottery is the idea of replacement. Take a 52-card deck to represent a lottery, with
the participant asked to chose a card as the “winning” card, such as the queen of
hearts. In the first choice, the king of diamonds is picked, and not reshuffled
back into the deck. After each choice, if the cards are not put back into the deck,
eventually, the participant’s chances of picking the queen of hearts gets better
and better. After all, the choices of cards in the deck become less; if one card is
left, the participant knows he or she will win.
But a regular lottery does not “reshuffle” the numbers. Instead, lotteries
chose from the same “group” of numbers each week, which makes it even more
difficult to win. There may be repetitions in winning numbers, but the odds of
winning are the same each time the lottery is played. For example, the odds of
winning a recent California Super Lotto game were 1 in 18 million. Thus, if a
person bought 50 lottery tickets a week, his or her chances of winning would be
once every 6,923 years.