Probability on a 0-to-1 Scale

Probability on a 0-to-1 Scale

1. Know the scale
   Probability is always a number from 0 to 1.

   • 0 means the event cannot happen.
   • 1 means the event is certain.
   • Values between 0 and 1 show how likely the event is.

2. Find the probability
   Use the usual rule:

   [ P(\text{event})=\frac{\text{number of favorable outcomes}}{\text{total number of equally likely outcomes}} ]

   Count carefully. The numerator is the number of outcomes that match the event, and the denominator is the total possible outcomes.

3. Simplify the result
   Write the fraction in lowest terms if needed. If the answer is a decimal, make sure it still stays between 0 and 1.

4. Check your answer
   Ask yourself: does the value make sense on the probability scale? It should never be negative or greater than 1. If the event is impossible, the answer should be 0; if it must happen, the answer should be 1.

5. Common mistake to avoid
   Do not count outcomes that are not equally likely, and do not forget to include all possible outcomes in the denominator.

Use this process for each exercise: identify the event, count favorable and total outcomes, divide, simplify, and verify the result is on the 0-to-1 scale.