Probability Basics

Probability

• Probability is a mathematical concept describing the likelihood of an event occurring.
• Measured on a scale from 0 to 1, with 0 representing impossibility and 1 certainty.
• A probability of 1/2 indicates an event is equally likely to happen or not.

Types of Events

• Events with probability less than 1/2 are unlikely.
• Events with probability greater than 1/2 are likely.

Probability Line

• The Probability Line visually represents event likelihood, with 0 (impossible) on the left and 1 (certain) on the right.
• Aids in understanding event probability visually.

Probability Calculations

• Probability can be expressed as fractions, decimals, or percentages.
• Calculated by dividing favorable outcomes by total possible outcomes.

Coin Toss

• Fair coin toss: heads (1/2) and tails (1/2) probability.
• Combined probability (heads + tails) equals 1.

Dice Roll

• Six-sided die: 6 possible outcomes, each with a probability of 1/6 (approximately 16.7%).
• Each number is equally likely to be rolled.

Trials and Experiments

• A trial (experiment) is a process with a random outcome (coin toss, die roll).
• Trial outcome is the result of a specific trial.
• More trials lead to results closer to expected probabilities.

Spinner Example

• Spinner with 16 equal sectors:
  • Probability of landing on 12 is 1/16 (approximately 6%).
  • Probability of landing on a blue sector (5 blue sectors) is 5/16 (approximately 31%).
  • Probability of landing on a yellow sector (11 yellow sectors) is 11/16 (approximately 69%).
  • Probabilities of all possible outcomes (blue + yellow) sum to 1.

Marble Example

• Bag with 3 green, 7 yellow, and 1 white marble:
  • Probability of drawing a green marble is 3/11 (approximately 27%).
  • Probability of drawing a yellow marble is 7/11 (approximately 64%).
  • Probability of drawing a white marble is 1/11 (approximately 9%).
  • Probabilities of all possible outcomes (green + yellow + white) sum to 1.

Key Takeaways

• Probability quantifies event likelihood.
• Multiple trials produce results closer to expected probabilities.
• The sum of probabilities for all possible outcomes is always 1.