Overview
This lecture explains how to determine the probability that a randomly selected student from a group earned an "A" on a test, using provided data.
Test Data Breakdown
- 30 students received an "A" (13 males, 17 females).
- 31 males and 37 females took the test, totaling 68 students.
Calculating Probability
- Probability of a random student getting an "A" = (number of "A" students) / (total students).
- Calculation: 30 / 68.
- Simplify the fraction by dividing numerator and denominator by 2: 15 / 34.
Decimal and Percentage Forms
- Convert fraction to decimal: 15 ÷ 34 ≈ 0.4412 (rounded to four decimal places).
- Convert decimal to percentage: 0.4412 × 100 = 44.12%.
- Fraction (15/34) gives the exact probability; decimal and percentage are approximations.
Key Terms & Definitions
- Probability — likelihood of an event occurring, calculated as (number of favorable outcomes) ÷ (total outcomes).
- Simplified Fraction — a fraction reduced to lowest terms, sharing no common factors except 1.
- Decimal — base-10 representation of a number, often rounded for convenience.
- Percentage — decimal number multiplied by 100 and expressed with a % sign.
Action Items / Next Steps
- Practice calculating probabilities in fraction, decimal, and percentage forms.
- Review rules for simplifying fractions.