Understanding Complementary Events Quiz

1) 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%).

2) 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).

3) 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).

4) 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).

5) 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).

6) 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).

7) 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).

8) 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).

9) 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).

10) 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).

11) 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).

12) 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).

13) 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.

14) 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).

15) 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).

16) 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).

17) 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).

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) 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.

20) 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).