Recording-2025-03-10T12:43:46.100Z

Probability Basics

• Probability of B given event A: This is denoted as P(B|A).

• Intersection concept: Refers to the situation where both event A and event B occur simultaneously.

  • Example: Choosing a group of women first and then taking a specific event A from that group.

Understanding Conditional Probability

• Conditional probability formula:

  • P(B|A) = P(A and B) / P(A)

  • This formula can be derived from counting the number of occurrences of events A and B relative to A alone.

Division of Fractions

• Process of dividing fractions: "Keep, Change, Flip"

  • Keep the first fraction.

  • Change the division sign to multiplication.

  • Flip the second fraction.

Independent Events

• Definition: Two events are independent if the occurrence of one event does not affect the probability of the other event.

• For independent events:

  • P(A and B) = P(A) * P(B)

Approval Ratings Example

• Example case: Approval rating of a specific group (18 to 39 year-olds) regarding same-sex marriage.

• Noted Probabilities:

  • P(Approval|Age Group) = 78%

Mutually Exclusive Events

• Definition: Two events are mutually exclusive if they cannot occur at the same time.

• Determining if events A and C are mutually exclusive.

  • Required to show examples or reasons.

Contingency Tables

• Overview: A Contingency Table displays the frequency of two categorical variables.

  • Example variables: Gender (Male, Female) and Grades (A, B, C, D).

• Evaluation Process:

  • Use specific cells to retrieve probabilities based on combinations from the table.

Example Cell Interpretation

• Specific cell value interpretation:

  • E.g., 43 means number of people who are male and right-handed.

• Calculating probabilities using table values:

  • For P(L and F), identify and divide the cell value by total.

  • Total values are represented with corresponding conditions from the table.