Lesson 10-1: Understand Probability

Property

When all possible outcomes have the same chance of occurring, the theoretical probability of an event is defined as:

Examples

• Rolling a die: On a standard 6-sided die, the probability of rolling an even number (2, 4, or 6) is $P(\text{even}) = \frac{3}{6} = \frac{1}{2}$.
• Spinning a spinner: For a spinner divided into 8 equal sections where 3 are red and 5 are blue, the probability of landing on red is $P(\text{red}) = \frac{3}{8}$.
• Random selection: If a bag contains 4 green marbles and 6 yellow marbles, the probability of drawing a green marble is $P(\text{green}) = \frac{4}{10} = \frac{2}{5}$ or $40\%$.

Explanation

When every possible outcome in a scenario has the exact same chance of occurring, they are known as equally likely outcomes. To calculate the probability of a specific event, you simply count the number of outcomes that match your event (the favorable outcomes) and divide it by the total number of possible outcomes. This mathematical ratio can then be written as a fraction, a decimal, or a percentage to represent the likelihood of the event happening.

Property

Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around $\frac{1}{2}$ indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. If $A$ is any event and $S$ is the sample space, then $0 \leq P(A) \leq 1$.

Examples

• The probability of a standard six-sided die landing on the number 9 is 0. This is an impossible event.
• The probability that an object dropped will fall down is 1. This is a certain event.
• When drawing a card from a standard 52-card deck, the probability of drawing a black card is $\frac{26}{52} = \frac{1}{2}$, an event that is equally likely as not.

Explanation

Probability is measured on a scale from 0 to 1. A probability of 0 means an event is impossible. A probability of 1 means it's certain. A probability of $\frac{1}{2}$ means it's equally likely to happen or not happen.