Probability: Certain, Likely, Unlikely, Impossible: Fifth Grade Mathematics
Probability measures the likelihood that a particular event will occur, spanning a continuum from impossible to certain.
The Probability Likelihood Continuum
Probability is described qualitatively using five standard likelihood terms, mapped across a probability scale from 0 to 1:
+--------------------------------------------------------------------------+
| THE PROBABILITY CONTINUUM |
| |
| 0 1/2 (0.50) 1 |
| <---+-------------------------+-------------------------+---> |
| Impossible Unlikely Equally Likely Likely Certain |
| (0% chance) (< 50% chance) (50% chance) (> 50% chance)(100% chance) |
+--------------------------------------------------------------------------+
Definitions of Qualitative Terms
- Impossible: The event can NEVER happen; probability = 0 (e.g., rolling an 8 on a standard six-sided die).
- Unlikely: The event has a chance of occurring, but it is less than half the time; probability between 0 and 1/2 (e.g., rolling a 1 on a six-sided die, 1/6 chance).
- Equally Likely (As likely as not): The event has an exact 50-50 chance; probability = 1/2 (e.g., flipping heads on a fair coin).
- Likely: The event has a strong chance of occurring, more than half the time; probability between 1/2 and 1 (e.g., rolling a number greater than 1 on a six-sided die, 5/6 chance).
- Certain: The event is GUARANTEED to happen; probability = 1 (e.g., rolling a number less than 7 on a standard six-sided die).
Exercises and Solutions
Exercise 1: Classifying Likelihood of Events. Assign one of the five likelihood terms (impossible, unlikely, equally likely, likely, certain) to each scenario: Event A: The sun will rise in the east tomorrow morning. Event B: A standard fair coin lands on tails. Event C: You draw a red marble from a bag containing 9 red marbles and 1 blue marble. Event D: You roll a standard die and land on a 9. Event E: You draw a green marble from a bag with 1 green and 8 yellow marbles.
Solution 1: Event A is Certain (guaranteed by astronomical reality). Event B is Equally Likely (exactly 1 out of 2 outcomes, 50% chance). Event C is Likely (9 out of 10 marbles are red, 90% chance). Event D is Impossible (a standard die only has numbers 1 through 6). Event E is Unlikely (only 1 out of 9 marbles is green, about 11% chance).
Exercise 2: Designing a Probability Spinner. Describe how to color an 8-section spinner so that: landing on Blue is Likely, landing on Red is Unlikely, and landing on Green is Impossible.
Solution 2: The spinner has 8 equal sections. For Blue to be Likely, it must occupy more than half of the spinner (> 4 sections); color 6 sections Blue. For Red to be Unlikely, it must occupy less than half of the spinner (< 4 sections); color 2 sections Red. For Green to be Impossible, it must occupy 0 sections; color 0 sections Green. On this spinner: Blue has a 6/8 (75%) chance (Likely), Red has a 2/8 (25%) chance (Unlikely), and Green has a 0/8 (0%) chance (Impossible).