Proportionality · TEKS 7.6A–E, 7.6H, 7.6I
Probability & predictions
Probability = favorable outcomes ÷ total outcomes. It is always between 0 and 1.
Key steps
- Sample space: list or tree diagram. Count with multiplication (3 shirts × 4 pants = 12 outfits).
- Complement: P(not A) = 1 − P(A).
- Independent events ("and"): multiply the probabilities.
- Theoretical uses what should happen; experimental uses what did happen.
- Predict: probability × number of trials.
Worked example
Flip a coin and roll a number cube. P(heads and a number > 4)?
- P(heads) = 1/2. P(5 or 6) = 2/6 = 1/3.
- Multiply: 1/2 × 1/3 = 1/6.
- Answer: 1/6
Watch out: For "and", multiply. Adding 1/2 + 1/3 gives 5/6, which is far too likely.
Practice
5 questions with new numbers every set. Get 4 of 5 to mark this topic as practiced.