Understanding Complementary Events Quiz

1) What is a complementary event?

An event and its 'not event' that together include all possible outcomes

Two events where one event is the opposite of the other

Two events that happen at the same time

Two events that have the same probability

Complementary events are an event and its complement; together they cover the whole sample space.

Explanation

Complementary events are an event and its complement; together they cover the whole sample space.

2) If the probability of rain tomorrow is 0.35, what is the probability that it will NOT rain?

0.35

0.65

0.70

1.35

(1 - 0.35 = 0.65).

Explanation

(1 - 0.35 = 0.65).

3) Which pair represents complementary events?

Rolling an even number and rolling a 6 on a die

Flipping heads and flipping tails on a coin

Drawing a red card and drawing a heart from a deck

Picking a vowel and picking the letter A

A single flip is either heads or tails; they are mutually exclusive and exhaustive.

Explanation

A single flip is either heads or tails; they are mutually exclusive and exhaustive.

4) The probability of an event A is 0.42. What is P(not A)?

0.58

0.52

0.42

1.00

(1 - 0.42 = 0.58).

Explanation

(1 - 0.42 = 0.58).

5) If (P(A) + P(not A) = 1), and (P(A) = 3/8), what is (P(not A))?

3/8

8/3

5/8

1/8

(1 - 3/8 = 5/8).

Explanation

(1 - 3/8 = 5/8).

6) A spinner has 8 equal sections. If (P(blue) = 2/8), what is (P(not blue))?

2/8

4/8

8/8

6/8

(1 - 2/8 = 6/8).

Explanation

(1 - 2/8 = 6/8).

7) Which statement is TRUE about complementary events?

They can both happen at the same time

Their probabilities always add up to 1

They always have equal probabilities

They are independent events

By definition (P(A) + P(not A) = 1).

Explanation

By definition (P(A) + P(not A) = 1).

8) A bag contains red and blue marbles. If (P(red) = 0.28), what is (P(blue))?

0.28

0.38

0.70

0.72

Only red/blue → (1 - 0.28 = 0.72).

Explanation

Only red/blue → (1 - 0.28 = 0.72).

9) If you flip a fair coin, what is (P(not heads))?

0.5

0.25

0

1

(1 - 0.5 = 0.5).

Explanation

(1 - 0.5 = 0.5).

10) The probability of selecting a defective light bulb is 0.03. What is the probability of selecting a light bulb that is NOT defective?

0.03

0.30

0.97

1.03

(1 - 0.03 = 0.97).

Explanation

(1 - 0.03 = 0.97).

11) What is the probability of spinning red?

1/10

2/10

4/10

3/10

Red occupies 3 of 10 sections → (3/10).

Explanation

Red occupies 3 of 10 sections → (3/10).

12) What is the probability of NOT spinning red?

7/10

4/10

3/10

10/10

(1 - 3/10 = 7/10).

Explanation

(1 - 3/10 = 7/10).

13) What is the probability of NOT spinning blue?

4/10

6/10

7/10

9/10

If blue is (1/10), then not blue = (1 - 1/10 = 9/10).

Explanation

If blue is (1/10), then not blue = (1 - 1/10 = 9/10).

14) If (P(green) + P(not green) = 1), which equation is correct?

2/10 + 6/10 = 1

2/10 + 8/10 = 1

2/10 + 7/10 = 1

2/10 + 2/10 = 1

(2/10) green → not green = (8/10); (2/10 + 8/10 = 1).

Explanation

(2/10) green → not green = (8/10); (2/10 + 8/10 = 1).

15) A student says, 'The probability of passing the test is 0.8, so the probability of not passing is 0.8 too.' What is wrong?

Nothing, the student is correct

The probabilities should both be 0.5

P(passing) should be 0.2, not 0.8

P(not passing) should be 0.2, not 0.8

Complements sum to 1 → (1 - 0.8 = 0.2).

Explanation

Complements sum to 1 → (1 - 0.8 = 0.2).

16) In a game, the probability of winning is (1/5). What is the probability of NOT winning?

1/5

2/5

4/5

5/5

(1 - 1/5 = 4/5).

Explanation

(1 - 1/5 = 4/5).

17) Which of the following is NOT a pair of complementary events?

Getting a 6 on a die and not getting a 6

Drawing an ace and not drawing an ace

Selecting a girl and not selecting a girl

Rolling an odd number and rolling a 3 on a die

“Odd” includes 3, so they’re not complements (not exhaustive/mutually exclusive pair).

Explanation

“Odd” includes 3, so they’re not complements (not exhaustive/mutually exclusive pair).

18) If an event is certain to happen, what is the probability of its complement?

0

0.5

1

Cannot be determined

If (P(A)=1), then (P(not A)=0).

Explanation

If (P(A)=1), then (P(not A)=0).

19) A weather forecast says there is a 15% chance of snow. What is the probability it will NOT snow?

15%

50%

85%

100%

(100% - 15% = 85%).

Explanation

(100% - 15% = 85%).

20) A jar contains only red and green jellybeans. If (P(green) = 0.44), what is (P(red))?

0.44

0.50

0.56

1.00

(1 - 0.44 = 0.56).

Explanation

(1 - 0.44 = 0.56).