Skip to content

1.8 Basic Probability

Key Concepts:

Probability:

  • Numerical measure of the likelihood of an event.
  • Ranges from 0 to 1:
  • 0: Event is impossible.
  • 1: Event is certain.
  • 0.5: Event is equally likely or unlikely.

Random Experiment:

  • A process with more than one possible outcome.
  • Example: Revenue outcomes for movies KGF (3, 4, 5, 6 lakhs) and Kantara (4, 5, 6 lakhs).

Sample Space (S):

  • Set of all possible outcomes of a random experiment.
  • Example: Combining outcomes for KGF and Kantara yields 12 outcomes in the sample space.

Event (A):

  • A subset of the sample space, representing outcomes of interest.
  • Example: Event A (KGF is a hit) includes outcomes where revenue is 5 or 6 lakhs.

Complement of an Event (A'):

  • Consists of all outcomes in the sample space not in event A.
  • Example: If A = {KGF is a hit}, then A' = {KGF is not a hit}.

Rules of Probability:

Assignment:

  • Probability of any outcome is between 0 and 1.
  • The sum of probabilities of all outcomes in the sample space is 1.

Calculating Event Probability:

  • Sum the probabilities of all outcomes within the event.
  • Example:
  • Event A: KGF is a hit (revenue ≥ 5 lakhs).
    • Outcomes: {5, 6 lakhs}.
    • Probabilities: 0.1 + 0.08 + … = 0.34.
  • Event B: Kantara is a hit (revenue ≥ 5 lakhs).
    • Outcomes: {5, 6 lakhs}.
    • Probabilities: 0.1 + 0.1 + … = 0.6.

Complement Rule:

  • \( P(A') = 1 - P(A) \).
  • Example:
  • For Event A: \( P(A) = 0.34 \) → \( P(A') = 1 - 0.34 = 0.66 \).
  • For Event B: \( P(B) = 0.6 \) → \( P(B') = 1 - 0.6 = 0.4 \).

Application Example:

KGF Revenue:

  • Possible values: 3, 4, 5, 6 lakhs.
  • Probability KGF is a hit (≥ 5 lakhs): 0.34.
  • Complement (not a hit): 0.66.

Kantara Revenue:

  • Possible values: 4, 5, 6 lakhs.
  • Probability Kantara is a hit (≥ 5 lakhs): 0.6.
  • Complement (not a hit): 0.4.

Visualization:

Venn Diagrams:

  • Sample space represented as a rectangle.
  • Events represented as circles.
  • Complements shown as the area outside the circle but inside the rectangle.
Ask Hive Chat Chat Icon
Hive Chat
Hi, I'm Hive Chat, an AI assistant created by CollegeHive.
How can I help you today?