To solve probability problems involving selecting a person with a certain trait or category, follow these core principles:
The probability of selecting someone with a specific trait is the ratio of people with the trait to the total number of people in the group:
[ \text{Probability} = \frac{\text{Number of people with the trait}}{\text{Total number of people in the group}} ]
Example:
If a class has 30 students and 12 are girls, the probability of randomly selecting a girl is:
[ \frac{12}{30} = 0.4 \quad (\text{or } 40\%) ]
When asked for the probability of selecting someone with Trait A or Trait B, use the addition rule to avoid double-counting those with both traits:
[ P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B) ]
Example:
In a group of 50 people:
Probability of left-handed OR wears glasses:
[ \frac{25}{50} + \frac{20}{50} - \frac{15}{50} = \frac{30}{50} = 0.6 \quad (\text{or }60\%) ]
Key Takeaway: Always start by identifying the total group size and the relevant counts for the trait(s) in question, then apply the appropriate formula. If you provide the specific numbers from your problem, I can help compute the exact answer!
Let me know if you have a concrete problem to solve—I’ll walk through it step-by-step.
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