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Probability
The probability is high that at least one question on
the SAT will cover probability. The probability is even higher that
the probability formula will help you on SAT probability questions.
Here’s the formula:
Let’s say you go on a game show and are put in a room
that contains 52 doors. Behind 13 of the doors are awesome prizes,
including new cars, diamond watches, and infinity millions of dollars.
Behind the rest of the doors are goats. What’s the probability that
you’ll draw an awesome prize?
And what’s the probability that you’ll end up with the
goat?
Here’s a more complicated example, involving the SAT’s
favorite probability prop: marbles! That SAT sure knows how to have
a good time with marbles.
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There are three ways for Joe to pick a green
marble (since there are three different green marbles),
but there are ten total possible outcomes (one for
each marble in the bag). Therefore, the probability of picking a
green marble is
When you calculate probability, always be careful to divide
by the total number of chances. In the last example, you may have
been tempted to leave out the three chances of picking a green marble
from the total possibilities, yielding P =
3/7 . Brutal
wrongness.
Backwards Probability
The SAT might also ask you a “backwards” probability question.
For example, if you have a bag holding twenty marbles, and you have
a 1/5 chance
of picking a blue marble, how many blue marbles are in the bag?
All you have to do is set up the proper equation, following the
model of P = m
/n :
in which x is the variable
denoting the number of blue marbles. Cross-multiplying through the
equation, you get 5x = 20., which reduces
to x = 4.
The Range of Probability
The probability, P, that
any event will occur is always 0 ≤ P ≤ 1. A probability of 0 for
an event means that the event will never happen.
A probability of 1 means the event will always occur.
Drawing a bouquet of flowers from a standard deck of cards has a
probability of 0. Becoming Lord (or Lady) of the Universe
after scoring 2400 on the new SAT has a probability
of 1.
The Probability That an Event Will Not Occur
Some SAT questions ask you to determine the probability
that an event will not occur. In that case, just
figure out the probability of the event occurring, and subtract that
number from 1.
Probability and Multiple Unrelated Events
More difficult SAT probability questions deal with multiple
unrelated events. For these questions, the probability of both events
occurring is the product of the outcomes of each event: 
, where 
is the probability of the first event,
and 
is the probability of the second
event.
, where is the probability of the first event,
and is the probability of the second
event.A perfect example of two unrelated events is this: Drawing
a spade from a full deck of cards and rolling a
one with a six-sided die is the product of the probability of each
event. Neither outcome will affect the outcome of the other. The
probability of both events occuring is
The same principle can be applied to finding the probability
of a series of events. Take a look at the following problem:
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In order to find the probability
of three consecutive events, first find the probability of each
event separately. The first jelly bean has a 15
/50 chance of being
licorice-flavored. The second jellybean, however, is a different
story. There are now only 49 jelly beans left in the jar, so the
probability of getting another licorice-flavored one is
14/49 .
The probability of getting a third licorice-flavored jelly bean
is 13/48 .
The odds of all three happening are:
The moral of this sad tale of larceny and candy is that
crime pays only 13/
560 of the time.
Geometric Probability
The new SAT occasionally asks questions to which it has
given the exciting name “geometric probability.” The SAT could have
saved itself some time by just saying that it’s going to ask you
questions about playing darts.
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Here you have to find the area of some shaded (or unshaded)
region, and divide that by the total area of the figure. In this
question, the dartboard is a circle of radius 3. The shaded region
is the area of the circle minus a circle of radius 2.
and 0.56 equals 56%.
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