Probability From a Spinner

Probability from a Spinner

1. Identify the favorable outcomes Look at the spinner and decide which sections match the event in the question. Count only those sections.

2. Count all equally likely outcomes Find the total number of sections on the spinner. If the sections are not all the same size, the probability may depend on the sizes; otherwise, use the count of equal sections.

3. Write the probability as a fraction

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

4. Simplify the fraction Reduce the fraction to lowest terms. If needed, divide numerator and denominator by their greatest common factor.

5. Check your answer Make sure the numerator is not larger than the denominator and that the fraction matches the spinner setup. A probability of 0 means the event cannot happen; a probability of 1 means it is certain.

Quick example method

If 3 sections out of 8 match the event, the probability is (\frac{3}{8}). If 4 out of 12 match, simplify (\frac{4}{12}) to (\frac{1}{3}).

Always read the spinner carefully before counting, then simplify the final fraction.