Probability: language, scale, calculation, expected outcomes

Probability: Language, Scale, Calculation, Expected Outcomes 🎲

1. Probability Language

Probability describes how likely an event is to happen. We use words such as:

• 🔹 Impossible – will never happen
• 🔹 Unlikely – not likely to happen
• 🔹 Even chance – as likely to happen as not
• 🔹 Likely – will probably happen
• 🔹 Certain – will definitely happen

2. Probability Scale

Probability is measured on a scale from 0 to 1 (or 0% to 100%).

3. Calculating Probability

For equally likely outcomes:

$P(A) = \frac{\text{Number of favorable outcomes}}{\text{Total number of equally likely outcomes}}$

1. 🔹 Identify the total number of possible outcomes.
2. 🔹 Count how many of those outcomes give the event you are interested in.
3. 🔹 Divide the favorable count by the total count.
4. 🔹 Express as a fraction, decimal, or percentage.

Example: Rolling a fair six‑sided die, probability of getting a 4:

$P(4) = \frac{1}{6} \approx 0.167 = 16.7\%$

4. Expected Outcomes

If an experiment is repeated $n$ times, the expected number of times an event $A$ occurs is:

$$E = n \times P(A)$$