Understanding Probability
Probability is the measure of how likely an event is to occur. It's expressed as a number between 0 and 1, where 0 means impossible and 1 means certain. Probabilities can also be expressed as percentages (0% to 100%) or fractions.
Basic Formula
P(A) = Favorable outcomes / Total outcomesRange
Probability always falls between 0 and 1 (or 0% and 100%)
Certainty
P = 0 (impossible), P = 0.5 (equally likely), P = 1 (certain)
Types of Probability
Simple Probability
The probability of a single event occurring.
Rolling a 4 on a six-sided die: P = 1/6 ≈ 0.167 or 16.7%
Compound Probability
The probability of two or more events occurring.
P(A and B) = P(A) × P(B)P(A or B) = P(A) + P(B)Conditional Probability
The probability of an event occurring given that another event has occurred.
P(A|B) = P(A and B) / P(B)Common Examples
Coin Flip
P(Heads) = 1/2 = 0.5 = 50%
Two equally likely outcomes
Drawing a Card
P(Ace) = 4/52 ≈ 0.077 = 7.7%
4 aces in a 52-card deck
Two Dice Sum
P(Sum = 7) = 6/36 ≈ 0.167 = 16.7%
Six ways to get 7 out of 36 outcomes
Weather Forecast
P(Rain) = 0.3 = 30%
Based on historical data and models
Frequently Asked Questions
What's the difference between theoretical and experimental probability?
Theoretical probability is calculated based on the possible outcomes (like 1/6 for rolling a specific number on a die). Experimental probability is based on actual trials (if you rolled a die 100 times and got a 4 twenty times, experimental probability = 20/100 = 0.2).
Can probability be greater than 1?
No, probability can never be greater than 1 (or 100%). A probability of 1 means the event is certain to happen. If you calculate a probability greater than 1, there's an error in your calculation.
What are independent events?
Independent events are events where the outcome of one does not affect the outcome of another. For example, flipping a coin twice - the first flip doesn't influence the second. With independent events, multiply probabilities: P(both heads) = 0.5 × 0.5 = 0.25.