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Door 10 · Grade 7

📊 Probability (Intro)

Probability is always between 0 and 1 (inclusive)

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Basic Probability & Likelihood Scale

Probability measures how likely an event is to occur. It ranges from 0 (impossible) to 1 (certain).
Formula: P(event) = Number of favorable outcomes / Total number of possible outcomes
Probability ValueMeaningExample0ImpossibleRolling a 7 on a standard die0 to 0.5UnlikelyRolling a 1 on a die (1/6)0.5Equally likelyFlipping heads on a coin0.5 to 1LikelyDrawing a red card from a deck1CertainSun rising tomorrowThe sum of probabilities of all possible outcomes always equals 1.

Worked example

Problem: A bag has 3 red, 2 blue, 5 green marbles. Find P(red), P(blue), P(black).

  1. Total = 10.
  2. P(red)=3/10=0.3.
  3. P(blue)=2/10=0.2.
  4. P(black)=0/10=0 (no black marbles).

Answer: P(black)=0/10=0 (no black marbles).

Experimental vs Theoretical Probability

There are two types of probability:
TypeDefinitionExampleTheoretical ProbabilityWhat SHOULD happen mathematicallyP(heads) = 1/2Experimental ProbabilityWhat ACTUALLY happens in trials48 heads in 100 flips => P = 0.48Law of Large Numbers: As the number of trials increases, experimental probability gets closer and closer to theoretical probability.
Experimental P = (number of times event occurred) / (total number of trials)

Worked example

Problem: A die is rolled 60 times. Number 3 appears 12 times. Find experimental P(3). Compare to theoretical.

  1. Experimental P(3) = 12/60 = 0.2.
  2. Theoretical P(3) = 1/6 ≈ 0.167.
  3. Very close!

Answer: Very close!