Sat math Essentials

a.
1
6
b.
1
3
c.
2
5
d.
1
2
e.
3
5
Answer
d.
This problem asks you to find the probability that two events will occur (picking a Fuji apple or pick-
ing a McIntosh apple), so you must add the probabilities of each event. So first find the probability that
someone will pick a Fuji apple:
the probability of picking a Fuji apple 
1
4
2
0
0
Now find the probability that someone will pick a McIntosh apple:
the probability of picking a McIntosh apple 
1
2
2
0
0
Now add the probabilities together:
1
4
2
0
0
1
2
2
0
0
1
6
2
0
0
1
2
The probability that someone will pick a Fuji apple or a McIntosh is 
1
2
.
20
40 + 24 + 12 + 24 + 20
number of McIntosh apples
total number of apples
40
40 + 24 + 12 + 24 + 20
number of Fuji apples
total number of apples
number of black buttons
total number of buttons
–
P R O B L E M S O LV I N G
–
1 7 0

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Helpful Hints about Probability
■
If an event is certain to occur, its probability is 1.
■
If an event is certain 
not
to occur, its probability is 0.
■
You can find the probability of an unknown event if you know the probability of all other events occurring.
Simply add the known probabilities together and subtract the result from 1. For example, let’s say there is a
bag filled with red, orange, and yellow buttons. You want to know the probability that you will pick a red
button from a bag, but you don’t know how many red buttons there are. However, you do know that the
probability of picking an orange button is 
2
3
0
and the probability of picking a yellow button is 
1
2
4
0
. If you add
these probabilities together, you know the probability that you will pick an orange or yellow button:
2
3
0
1
2
6
0
1
2
9
0
. This probability,
1
2
9
0
, is also the probability that you 
won’t
pick a 
red
button. Therefore, if you subtract
1 
1
2
9
0
, you will know the probability that you 
will
pick a red button. 1 
1
2
9
0
2
1
0
. Therefore, the probabil-
ity of choosing a red button is 
2
1
0
.
Practice Question 
Angie ordered 75 pizzas for a party. Some are pepperoni, some are mushroom, some are onion, some are
sausage, and some are olive. However, the pizzas arrived in unmarked boxes, so she doesn’t know which
box contains what kind of pizza. The probability that a box contains a pepperoni pizza is 
1
1
5
, the probabil-
ity that a box contains a mushroom pizza is 
1
2
5
, the probability that a box contains an onion pizza is 
1
7
6
5
, and
the probability that a box contains a sausage pizza is 
2
8
5
. If Angie opens a box at random, what is the proba-
bility that she will find an olive pizza?