Why can’t a probability be negative?

Answer: A probability represents the likelihood or chance of an event occurring, and it is inherently a non-negative value.

Here’s an explanation:

1. Relative Frequency: Probability is often defined as the long-term relative frequency of an event occurring in a large number of trials. For example, if you flip a fair coin many times, the probability of getting heads is the proportion of times heads occur relative to the total number of flips. Since the number of times an event occurs cannot be negative, probability is inherently non-negative.
2. Proportion of Outcomes: In probability theory, the probability of an event is typically calculated as the ratio of the number of favorable outcomes to the total number of possible outcomes. For instance, when rolling a fair six-sided dice, the probability of rolling a 4 is 1 out of 6 because there is one favorable outcome (rolling a 4) out of six possible outcomes (rolling a number from 1 to 6). Again, both the number of favorable outcomes and the total number of possible outcomes cannot be negative, ensuring that probability remains non-negative.
3. Interpretation as Likelihood: Probability is often interpreted as a measure of likelihood or chance. A probability of 0 implies impossibility (the event cannot occur), while a probability of 1 indicates certainty (the event is guaranteed to occur). Values between 0 and 1 represent varying degrees of likelihood, with higher values indicating higher likelihood and lower values indicating lower likelihood. Since likelihood cannot be negative, probability must be non-negative.

In summary, probability is inherently a non-negative value because it represents the relative frequency or proportion of favorable outcomes in relation to the total number of possible outcomes, and it is interpreted as the likelihood or chance of an event occurring.