that both xand ywill occur is given by the product of their separate probabilities; and
the probability that either of the two events will occur is given by the sum of their sep-
arate probabilities minus the probability that both will occur. For example, if the prob-
ability that a certain man will live to be 70 is 0.5, and the probability that his wife will
live to be 70 is 0.6, the probability that they will both live to be 70 is 0.5 0.6 0.3;
the probability that either the husband or wife will reach 70 is 0.5 0.6 0.3 0.8.What are the definitionsof chance?
Chance is defined in many ways. For example, chance means opportunity to some, or
the chance to do something. Chance can also mean luck or fortune, such as running
into someone one has not seen in years by “pure chance.” Chance also involves taking
a risk, which may include some type of danger.
Mathematically speaking, chance is a measure of how likely it is that an event will
occur—in other words, a probability. For example, if a meteorologist says that a hurri-
cane on a certain path has struck the coast of Florida, say, about 4 times out of 10,
then the ratio becomes 4 to 10, with the chance of striking under the same conditions
being 40 percent.What do the terms randomand stochasticmean in probability?
When speaking about probability, the term randommeans the outcomes of an experi-
ment have the same probability of occurring. Because of this, the outcome of the
experiment produces a random sample.
Random also is commonly thought of as being synonymous with stochastic,
which is from the Greek word meaning “pertaining to chance.” It is usually used to
indicate a particular subject seen from the point of view of randomness. Stochastic is
248 often thought of as the “opposite” of deterministic,a term that means random phe-
What is the probability of drawing a diamond card
or an ace from a pack of 52 playing cards?T
he probability of drawing a diamond-faced card from a pack of 52 playing
cards is easy to determine. Since there are 13 diamond-faced cards in the
deck, the probability becomes 13/52 1/4 0.25.The probability of drawing an ace from a pack of 52 playing cards is also easy
to determine. There are 4 aces in the deck of 52 cards; thus, the probability
becomes 4/52 1/13 0.076923. This represents a much lower probability
than drawing a card in a specific suit, illustrated in the preceding example.