Question

when you are determining the probability of an event, why must the probability be between 0 and 1? explain your answer.

Explanation:

Probability measures the likelihood of an event. An event with probability 0 is impossible (e.g., rolling a 7 on a standard 6 - sided die). An event with probability 1 is certain (e.g., a coin flip resulting in heads or tails). For any event, the number of favorable outcomes (let's say \(n\)) and the total number of possible outcomes (let's say \(N\)) satisfy \(0\leq n\leq N\). The formula for probability \(P=\frac{n}{N}\). When \(n = 0\), \(P = 0\); when \(n=N\), \(P = 1\); and for values of \(n\) between 0 and \(N\), \(P\) is between 0 and 1. So probability must lie in this range as it represents the proportion of favorable to total possible outcomes.

Answer:

Probability is the ratio of the number of favorable outcomes (\(n\)) to the total number of possible outcomes (\(N\)) (\(P=\frac{n}{N}\)). Since \(0\leq n\leq N\) (you can't have fewer favorable outcomes than 0 or more than the total possible), dividing \(n\) by \(N\) gives a value between 0 (impossible event, \(n = 0\)) and 1 (certain event, \(n=N\)).