Understanding Probability Basics
Probability always ranges from 0 to 1, and all probabilities in a set of possible outcomes must add up to exactly 1. This fundamental rule helps us check if we've accounted for all possibilities in a problem.
Mutually exclusive events are outcomes that cannot occur simultaneously. For example, when flipping a coin, it cannot be both heads and tails at once. When calculating probabilities involving mutually exclusive events, we use the "Or" rule: P(A or B) = P(A) + P(B).
For events that can overlap (non-mutually exclusive), we adjust our calculation to avoid counting the overlap twice: P(A or B) = P(A) + P(B) - P(A and B).
Remember this: The basic probability formula is simply the number of successful outcomes divided by the total number of possible outcomes.
When working with probability, you'll often need these key formulas:
- Expected frequency = total number of tries × probability
- Relative frequency = how many times an event occurs ÷ total number of trials
Probability trees can help visualize multiple events. For example, in consecutive tests with different passing probabilities (0.7 for the first test, 0.8 for the second), you can calculate outcomes like passing both tests: 0.7 × 0.8 = 0.56 or 56%.