UNDERSTANDING OF PROBABILITY || GRADE 11 STATISTICS AND PROBABILITY Q3

Understanding Probability

• Probability is the mathematical study of chance—the likelihood that an event will occur.
• An experiment is an activity whose result cannot be known with certainty in advance. Repeating an experiment is called a trial.
• An outcome is a result of an experiment.
• An event is a collection of one or more outcomes. A simple event contains just one possible outcome.
• The sample space is the set of all possible outcomes for an experiment.

Basic Probability Formula

When all outcomes are equally likely:

[ P(\text{event}) = \frac{\text{number of outcomes in the event}} {\text{total number of possible outcomes}} ]

Examples

• Rolling a die: The sample space is ({1,2,3,4,5,6}).

  • Rolling a 3: (1/6)
  • Rolling an even number (2, 4, or 6): (3/6 = 1/2)
  • Rolling a 0: (0), because 0 is not a possible outcome
  • Rolling a number greater than 4 (5 or 6): (2/6 = 1/3)
  • Rolling a number between 0 and 7 (1 through 6): (6/6 = 1)

• Tossing a coin: The sample space is ({\text{heads}, \text{tails}}). The probability of heads is (1/2), or 50%.

• Drawing a card from a standard 52-card deck:

  • Black cards: 26 of 52, so (26/52 = 1/2)
  • Face cards (jacks, queens, and kings): 12 of 52, so (12/52 = 3/13)
  • Cards that are not face cards: 40 of 52, so (40/52 = 10/13)

Clarifications

• The subtitles describe the chance of rain or a class suspension as 50% simply because there are two stated possibilities. Having two possible outcomes does not by itself mean they are equally likely.
• The subtitles give an incorrect simplification for the face-card probability. (12/52) simplifies to (3/13), not (3/1).

Speakers and Sources

• Speaker: One instructor/narrator presenting the lesson.
• Source/channel: WOW MATH.