Basic Chance: Certain, Likely, Unlikely, and Impossible Events - Third Grade Mathematics

In life, we cannot always predict the future with complete certainty. Will it rain tomorrow? Will you flip a coin and get heads? Will you draw a red marble from a bag of mixed colors? The mathematical study of chance and likelihood is called probability. In this chapter, you will discover the probability scale and learn how to classify future events as certain, likely, equally likely, unlikely, or impossible.

The Probability Scale

Probability measures how likely an event is to happen. We use five essential mathematical vocabulary terms to describe chance:

IMPOSSIBLE       UNLIKELY       EQUALLY LIKELY       LIKELY       CERTAIN
    |               |                 |                 |            |
0% Chance      Small Chance      50/50 Chance      Great Chance  100% Will
Cannot happen  Probably won't    Could go either   Probably      Happen!
                                 way               will happen

Defining the Five Likelihood Words

Let us define each term with everyday real-world examples:

1. Certain

An event that is 100% guaranteed to happen. There is no other possible outcome.
- Example: The sun will rise in the east tomorrow morning.

- Example: If a jar contains only green marbles, drawing a green marble is certain!


2. Likely

An event that has a very strong chance of happening, but is not completely guaranteed.
- Example: If a spinner has 7 blue sections and 1 yellow section, landing on blue is likely.

- Example: It is likely to snow during winter in Antarctica.


3. Equally Likely (As Likely As Not)

Two or more outcomes have the exact same chance of occurring (a 50/50 chance).
- Example: Flipping a fair coin and getting heads vs. getting tails.

- Example: Rolling an even number vs. an odd number on a standard 6-sided die.


4. Unlikely

An event that could happen, but has only a small chance of occurring.
- Example: Landing on the 1 yellow section on a spinner that has 7 blue sections.

- Example: Finding a four-leaf clover on your first step in a field.


5. Impossible

An event that has zero chance of happening. It can NEVER occur under any circumstances.
- Example: Rolling the number 8 on a standard 6-sided die numbered 1 through 6.

- Example: A fish walking down the street to the grocery store.

- Example: Drawing a red marble from a bag containing only blue marbles.


Analyzing Chance with Marble Bags

Imagine a mystery bag filled with colored marbles:

Bag Contents:
8 Red Marbles       1 Blue Marble       0 Green Marbles
Total = 9 marbles

If you close your eyes and draw one marble at random:
- Drawing a Red marble is LIKELY (8 out of 9 marbles are red!).

- Drawing a Blue marble is UNLIKELY (only 1 out of 9 marbles is blue).

- Drawing a Green marble is IMPOSSIBLE (there are 0 green marbles in the bag).

- Drawing a marble that is either Red or Blue is CERTAIN (every marble in the bag is red or blue).


Spinners and Fairness

A game is fair when all players have an equally likely chance of winning.

Fair Spinner:                      Unfair Spinner:
+---------------+                  +---------------+
|     Red       |                  |     Red       |
|     1/2       |                  |     3/4       |
+---------------+                  +-------+-------+
|    Blue       |                  | Blue  | Green |
|     1/2       |                  | 1/8   | 1/8   |
+---------------+                  +-------+-------+
Equally likely (Fair!)             Red is much more likely! (Unfair)

Chapter Practice Exercises

  1. Classify each event as Certain, Likely, Equally Likely, Unlikely, or Impossible: a. You roll a standard 6-sided die and roll a number between 1 and 6. b. You flip a coin and land on tails. c. You pull a blue sock from a drawer that contains 9 blue socks and 1 white sock. d. You pull a white sock from the same drawer (9 blue, 1 white). e. A live elephant flies through the air using its ears.
  2. A bag contains 5 red cubes and 5 yellow cubes. Is drawing a red cube more likely, less likely, or equally likely as drawing a yellow cube?
  3. Design a spinner with 4 sections where landing on Green is impossible, landing on Blue is likely, and landing on Yellow is unlikely.
  4. A standard die has numbers 1, 2, 3, 4, 5, 6. a. What is the likelihood of rolling an even number? b. What is the likelihood of rolling a 7? c. What is the likelihood of rolling a number less than 6?
  5. A student says: "Since there are only two outcomes (it will rain tomorrow or it won't rain), the chance of rain is always 50/50." Explain why the student is mistaken.

Solutions and Step-by-Step Answers

  1. Event classifications: a. Certain (all faces on a standard die are numbers 1 through 6). b. Equally likely (50% chance of tails, 50% chance of heads). c. Likely (9 out of 10 socks are blue). d. Unlikely (only 1 out of 10 socks is white). e. Impossible (elephants cannot fly).
  2. Equally likely. There are 5 red cubes and 5 yellow cubes, so both colors have the exact same chance of being picked.
  3. Sample spinner:
  4. Make a spinner with 4 sections total.
  5. Color 3 sections Blue (making Blue likely).
  6. Color 1 section Yellow (making Yellow unlikely).
  7. Do not color any sections Green (making Green impossible).
  8. Standard die: a. Rolling an even number (2, 4, 6) is equally likely (3 evens vs. 3 odds). b. Rolling a 7 is impossible (there is no 7 on a standard die). c. Rolling a number less than 6 (1, 2, 3, 4, 5) is likely (5 out of 6 outcomes).
  9. The student is confusing the number of possible outcomes with their probability. Just because there are two possibilities does not mean they have equal chances! For example, if you live in the middle of a desert where it only rains 3 days a year, the chance of rain is very unlikely, not 50/50.