7th Grade Math

Lesson 1A Probability 431

In Example 2, either Simone will go first or she will not go first.

These two events are complementary events. Two events are

complementary events if they are the only two possible outcomes.

The sum of the probabilities of an event and its complement is 1 or

100%. In symbols, P(A) + P(not A) = 1.

Complementary Events

TALENT COMPETITION Refer to Example 2. Find the probability

that Simone will not choose the song.

P(A) + P(not A) = 1 Definition of complementary events

_ 61 + P(not A) = 1 Replace P(A) with _ 61.

• 61 = - 61 Subtract _^16 from each side.

P(not A) = ^56 1 - 61 is 66 -^16 or _^56

SCHOOL Ricardo’s teacher uses a spinner

6

52

4 3

similar to the one shown at the right to^1

determine the order in which each group

will make its presentation. Use the spinner

to find each probability. Write as a fraction

in simplest form.

h. P(not group 4) i. P(not group 1 or group 3)

Complement of an Event Complement of an Event

The probability that event A

will not occur is noted as

P(not A). Since P(A) +

P(not A) = 1, P(not A) =

1 - P(A). P(not A) is read

as the probability of the

complement of A.

Use the spinner to find each probability. Write as a

RO

S N

Q P

T M

P

fraction in simplest form, a decimal, and a percent.

Example 1

1. P(M) 2. P(Q or R) 3. P(vowel)

MARBLES Roberto has a bag that contains 7 blue,

5 purple, 12 red, and 6 orange marbles. Find each

probability if he draws one marble at random from

the bag. Write as a fraction in simplest form.

Examples 2 and 3

4. P(purple) 55 P(red or orange) 6. P(green)


5. P(not blue) 8. P(not red or orange) 9. P(not yellow)


6. SURVEYS Shanté asked her classmates how many Number
   of Pets Response
   None 6
   1–2 15
   3 or more 4

pets they own. The responses are in the table. If a

student in her class is selected at random, what is

the probability that the student does not own 3 or

more pets? Write as a fraction in simplest form.

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