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Compare probabilities

Compare the likelihood of events by determining and comparing their probabilities, often represented as fractions, decimals, or points on a 0-to-1 scale. For equally likely outcomes, interpret probability as the fraction of outcomes that satisfy an event, and reason that a larger favorable fraction indicates a more likely event, while equal fractions indicate equally likely events; conditional probability and more advanced probability models are outside this scope.

Detailed Explanation: Compare probabilities

To compare the likelihood of two events:

  1. Find the probability of each event.
  2. Write each probability as a fraction:
Probability=number of favorable outcomestotal number of equally likely outcomes\text{Probability}=\frac{\text{number of favorable outcomes}}{\text{total number of equally likely outcomes}}
  1. Compare the fractions. The larger fraction represents the more likely event. Equal fractions mean the events are equally likely.

Example: A bag has 10 equally likely marbles:

  • 4 red marbles
  • 3 blue marbles
  • 3 green marbles

Which is more likely: drawing a red marble or a blue marble?

Step 1: Find each probability.

There are 4 red marbles out of 10:

P(red)=410P(\text{red})=\frac{4}{10}

There are 3 blue marbles out of 10:

P(blue)=310P(\text{blue})=\frac{3}{10}

Step 2: Compare the probabilities.

The fractions have the same denominator, so compare their numerators:

4>34>3

Therefore,

410>310\frac{4}{10}>\frac{3}{10}

Answer: Drawing a red marble is more likely than drawing a blue marble.

Learn by doing: Compare probabilities

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    Likelihood - One Die - Most Or Least Likely Event

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