Probability
Usually, about two questions on each SAT cover the topic
of probability. To begin to deal with these questions you first
have to understand what probability is:
For example, let’s say you’re on a game show and are shown
three doors. Behind one door there is a prize while behind the other
two doors are big piles of nothing. The probability that you will
choose the door with the prize is 1
/3, because out of
the three possibilities, there is one chance that you will pick
the correct door.
How about a more detailed example?
|
|
|
Joe
has 3 green marbles, 2 red marbles, and 5 blue marbles, and if all
the marbles are dropped into a dark bag, what is the probability
that Joe will pick out a green marble? |
|
There are 3 ways for Joe to pick a green
marble (since there are 3 different green marbles), but
there are 10 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 the incorrect
equation P = 3
/7.
Backward Probability
The SAT might also ask you a “backward” 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:
and
x is the variable denoting
the number of blue marbles. Cross-multiplying through the equation,
you get
, which reduces to
Combinations
Combination questions are more rarely found on the SAT
than probability questions. Still, they do occasionally show up,
so we cover them here. You can think of combination problems as
half-probability problems. These questions give you a situation
and ask you to figure out the total number of outcomes that can
arise from that situation. Whereas for probability questions you
have to figure out the likelihood of one outcome in comparison to
the total outcomes, in combination problems you only have to figure
out the total number of outcomes. For example:
|
|
|
Imagine
a man (or, if you want, a woman). To make things interesting, let’s
make him a naked man who wants to put on a pair of pants and a shirt.
He has 6 pairs of pants and 3 shirts. How many different outfits does
he have to choose from? |
|
To answer this question you have to figure out how many
different combinations of shirts and pants the man can make. To
do this, multiply the total number of object
1 (
6 pants)
by the total number of object
2 (
3 shirts).
Total outfits
= 
= 18.
If the man also had
4 hats, to calculate
the total number of outfits he could make you would multiply
= 72 total
outfits—that’s over
two months of outfits!
