Ctrl+k

Compare probabilities

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.

Detailed Explanation: Compare probabilities

To compare two probabilities, compare their values between 00 and 11:

  • The probability closer to 11 is more likely.
  • The probability closer to 00 is less likely.
  • If the values are equal, the events are equally likely.

When probabilities are fractions, compare the whole fractions—not just their numerators. You can rewrite them with a common denominator.

Example:
A bag has 88 equally likely marbles. Event AA is picking a blue marble, with probability

P(A)=38.P(A)=\frac{3}{8}.

Event BB has probability

P(B)=14.P(B)=\frac{1}{4}.

Which event is more likely?

Step 1: Use a common denominator.

Rewrite 14\frac{1}{4} with denominator 88:

14=28.\frac{1}{4}=\frac{2}{8}.

Step 2: Compare the probabilities.

Now compare:

38and28.\frac{3}{8} \quad \text{and} \quad \frac{2}{8}.

Since (3>2)(3>2),

38>28.\frac{3}{8}>\frac{2}{8}.

Conclusion: Event AA is more likely than Event BB. Although both probabilities are fractions, their numerators could not be compared until the denominators were the same.

Learn by doing: Compare probabilities

Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill

Practice with unlimited practice problems

Likelihood - One Die - Most Or Least Likely Event


    ?