Probability and Sample Spaces

Probability Calculations

Simple Probability Example (5/16)

• Calculating the probability of an event.
• Example: The probability is 5 over 16 (\frac{5}{16}).
• Since \frac{5}{16} cannot be simplified further, it remains as \frac{5}{16}.

Probability of Rolling an Even Number

• Identify even numbers within a set of outcomes, example rolling a 16 sided dice.
• For instance, with numbers up to 16, the even numbers are: 2, 4, 6, 8, 10, 12, 14, and 16.
• Total number of desired outcomes (even numbers) is counted.

Probability of "Not" an Event

• Scenario: A pencil box contains 5 red, 12 blue, 10 green, and 3 yellow markers.
• Problem: Find the probability of choosing a marker that is not yellow.
• Solution: Consider only the markers that are not yellow (red, blue, and green).
• Total number of non-yellow markers: 5 (red) + 12 (blue) + 10 (green) = 27.

Sample Space and Tree Diagrams

• Finding the sample space for a given question.
• Using tree diagrams as a method (often introduced in elementary or middle school).

Example: Flipping a Coin Two Times

• First Flip: A coin has two possible outcomes: heads or tails.

• Second Flip: After the first flip, another flip occurs.

  • If the first flip was heads, the second flip can be either heads or tails.
  • If the first flip was tails, the second flip can also be either heads or tails.