Math Problem Statement

What is the probability that the spinner lands on a number less than 7?

Solution

The question asks for P(<7)P(<7), the probability that the spinner lands on a number less than 7.

Total possible outcomes:

The spinner has 12 equal sections, numbered 1 through 12. This means there are 12 possible outcomes in total.

Favorable outcomes:

Numbers less than 7 are 1,2,3,4,5,61, 2, 3, 4, 5, 6. This gives 6 favorable outcomes.

Probability calculation:

P(<7)=Favorable outcomesTotal outcomes=612=12P(<7) = \frac{\text{Favorable outcomes}}{\text{Total outcomes}} = \frac{6}{12} = \frac{1}{2}

Final Answer:

P(<7)=0.5 or 50%P(<7) = 0.5 \text{ or } 50\%

Would you like additional details or have further questions?


Here are 5 related questions to explore the concept:

  1. What is the probability of landing on an even number with this spinner?
  2. What is P(>8)P(>8) for this spinner?
  3. If the spinner is spun twice, what is the probability that both spins result in numbers less than 7?
  4. How would the probability change if the spinner had 15 sections instead of 12?
  5. What is the probability of landing on a prime number?

Tip: When calculating probabilities, always ensure the total number of outcomes is correctly determined, especially for equally likely events!

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Math Problem Analysis

Mathematical Concepts

Probability
Counting Outcomes

Formulas

P(<7) = Favorable outcomes / Total outcomes

Theorems

Basic Probability Theory

Suitable Grade Level

Grades 5-7