THE TRANSITION LINE // FIELD NOTES // STOP 28
Probability, inequalities, and prime reduction
Field Book
Lessons 105 to 108
Method
Pencil and paper. Calculators never.
Room 7 opens this stop. The odds post at the window before every draw. Probability counts chosen outcomes over total outcomes, inequalities graph with a boundary, a fill choice, and a direction, capacity units convert by unit multipliers, and stubborn fractions reduce through their prime factors.
What you have to be able to do
- Compute the probability of a simple event
- Graph an inequality on the number line
- Convert capacity units
- Reduce a fraction by prime factorization
The procedures
ProbabilityField Book Lesson 105
- P(E) is the number of outcomes chosen over the total number of outcomes.
- Write it as a reduced fraction.
Inequalities on the lineField Book Lesson 106
- Mark the boundary number. Filled dot when it is included, open when it is not.
- Shade the direction the symbol claims.
Capacity conversionsField Book Lesson 107
- Build a unit multiplier from the capacity facts: gallons, quarts, pints, cups, liters, milliliters.
- Disappearing unit on the bottom, then multiply.
Reducing by primesField Book Lesson 108
- Prime factor the top and the bottom separately.
- Cancel every factor that appears in both, and multiply what remains.
Worked: one draw
- 5 red marbles among 20: P(red) = 520.
- Reduced: 14.
Worked: primes clear the fraction
- 180210 = (2 · 2 · 3 · 3 · 5) ÷ (2 · 3 · 5 · 7)
- Cancel 2, 3, and 5: 67 remains.
Terms on the record
| Term | Meaning |
|---|
| probability | the chance of an event: outcomes chosen over total outcomes |
| outcome | one possible result of a chance event |
| inequality | a claim that one side is larger or smaller than the other |
| boundary | the number where an inequality's shading begins |