Summary
Highlights
Probability represents the likelihood of an event occurring, calculated by comparing the number of favorable outcomes to the total number of outcomes. It can be expressed as a fraction, decimal, or percentage. For example, a 20% chance of rain means 20 out of 100 chances, which simplifies to 1/5 or 0.2.
There are two main types: theoretical probability, found using mathematics, and experimental probability, found by conducting an experiment. The total number of outcomes is called the sample space, and the favorable number of outcomes is called the event.
Using a bag of marbles numbered one through eight as an example, the video demonstrates calculating probabilities. The probability of selecting a 2 is 1/8 (0.125 or 12.5%). The probability of selecting an odd number (1, 3, 5, 7) is 4/8 or 1/2 (0.5 or 50%). The probability of selecting a number greater than 6 (7, 8) is 2/8 or 1/4 (0.25 or 25%).
The complement of an event is the probability that the event will not happen. The sum of the probability of an event occurring and the probability of it not occurring always equals 1 (or 100%). If P(E) is the probability of an event, then the probability of its complement, P(E'), is 1 - P(E).
Using a standard six-sided die, the probability of rolling a two is 1/6. The probability of not rolling a two (the complement) can be found by counting non-two outcomes (5/6) or by calculating 1 - 1/6, both yielding 5/6.
For a standard 52-card deck, the probability of drawing a face card (Jack, Queen, King of four suits, so 12 cards) is 12/52, which simplifies to 3/13. The probability of drawing a five (four fives in the deck) is 4/52, or 1/13. The probability of drawing a non-face card (the complement of a face card) is 1 - 3/13 = 10/13, or directly calculating 40 non-face cards out of 52, which also simplifies to 10/13.