Comparing probabilities involves determining which of two events is more likely, less likely, or equally likely by interpreting their values between 0 and 1. For equally likely outcomes, learners compare probabilities expressed as fractions, decimals, or percents—often by using equivalent forms or common denominators—and connect these values to favorable outcomes relative to total possible outcomes, rather than comparing numerators alone. This understanding excludes conditional probability, dependent events, and formal probability distributions.
To compare two probabilities, compare their values between and :
When probabilities are fractions, compare the whole fractions—not just their numerators. You can rewrite them with a common denominator.
Example:
A bag has equally likely marbles. Event is picking a blue marble, with probability
Event has probability
Which event is more likely?
Step 1: Use a common denominator.
Rewrite with denominator :
Step 2: Compare the probabilities.
Now compare:
Since ,
Conclusion: Event is more likely than Event . Although both probabilities are fractions, their numerators could not be compared until the denominators were the same.
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