Theoretical Probability Statistics Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

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

Solution

  1. 1
    Step 1: The die has 6 outcomes, the coin has 2 outcomes. Total outcomes = 6×2=126 \times 2 = 12.
  2. 2
    Step 2: Favourable outcome: (3, H) — only 1 outcome.
  3. 3
    Step 3: P(3 and H)=112P(3 \text{ and H}) = \frac{1}{12}.

Answer

112\frac{1}{12}
When two independent events occur together, the total sample space is the product of individual sample spaces. The multiplication principle is foundational for computing combined probabilities.

About Theoretical Probability

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.

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More Theoretical Probability Examples

Example 1 medium

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

Example 3 medium

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

Example 4 medium

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

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