354 MCGRAW-HILL’S SAT
Probability Geometrical Probability
Lesson 6: Probability Problems
A probability is a number between 0 and 1 that
represents the likelihood of an event. An event
with a probability of 0 is impossible, and an
event with a probability of 1 is certain. Most
probabilities, of course, are somewhere in
between 0 and 1. For instance, the probability
of rolling a 5 on a fair die is^1 ⁄ 6. It’s best to think
of a probability as a part-to-whole ratio. There
are six possible outcomes when you roll a die
(the whole), but only one of them is 5 (the part).
Thus, the probability of rolling a 5 is^1 ⁄ 6.Example:
What is the probability of rolling a sum of 5 on
two dice?
Here is a table showing all the possible sums on a roll
of two dice:
Clearly, there are four ways of getting a sum of 5 out
of a possible 36, so the probability is^4 ⁄ 36 , or^1 ⁄ 9.
Die 1Die 2142365123456
2345673456784567895678910678910117 8 9 10 11 12An SAT question may ask you to find the prob-
ability that something hits a certain region,
like a dart hitting a dartboard. In these situa-
tions, the probability is just the ratio of the par-
ticular area to the entire area.Example:
A landing target for skydivers consists of two con-
centric circles. The smaller circle has a radius of
3 meters, and the larger one has a radius of 6 meters.
If a skydiver hits the target, what is the probability
that she hits the smaller circle?
It might help to sketch the target:If she hits the target, then she hits an area that is
π(6)^2 = 36 πsquare meters in area. The smaller circle,
though, is only π(3)^2 = 9 πsquare meters in area, so the
probability that she lands within the smaller region
should be just 9π/36π=1/4.3
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