Theoretical Probability Statistics Example 1

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Example 1

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

Solution

  1. 1
    Step 1: List all outcomes: {HH, HT, TH, TT} — 4 equally likely outcomes.
  2. 2
    Step 2: Outcomes with exactly one head: {HT, TH} — 2 favourable outcomes.
  3. 3
    Step 3: P(exactly one head)=24=12P(\text{exactly one head}) = \frac{2}{4} = \frac{1}{2}.

Answer

12\frac{1}{2}
Theoretical probability uses the sample space of all equally likely outcomes. By listing every possibility, we can count favourable outcomes systematically.

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 2 medium

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

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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