Practice Theoretical Probability in Statistics

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

Theoretical probability is the expected probability of an event calculated by mathematical reasoning about equally likely outcomes, without conducting experiments. It equals the number of favorable outcomes divided by the total number of possible outcomes.

For a fair coin, you KNOW heads is \frac{1}{2} without flipping. You calculate based on logic: 1 favorable outcome (heads) out of 2 possible outcomes. That's theoretical - it's what SHOULD happen.

Example 1

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Two fair coins are tossed. Find the theoretical probability of getting exactly one head.

Example 2

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A fair die and a fair coin are used together. What is the probability of rolling a 3 AND getting heads?

Example 3

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A bag has 4 red and 6 blue balls. One ball is drawn, replaced, and a second is drawn. What is the probability both are red?

Example 4

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Two fair six-sided dice are rolled. What is the theoretical probability that the sum is 7?
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