O Level MathematicsC8.1 Probability concepts (likelihood, $P(A)$).

🎲 Rolling into Probability! Mastering Likelihood & P(A)

Edudent Academy
28 Jan 26

Probability is the mathematics of uncertainty: it tells us how likely events are to happen. **Understanding probability helps you make informed predictions** in exams, games and real-life decisions, so mastering P(A)P(A) is essential for O Level success.

What Does Probability Really Mean?

For any event AA, the probability P(A)P(A) is a number between 0 and 1. **A value of 0 means the event is impossible, while 1 means it is certain.** Everything else lies on this scale of likelihood. The basic rule is
P(A)=number of favourable outcomestotal number of equally likely outcomes.P(A)=\frac{\text{number of favourable outcomes}}{\text{total number of equally likely outcomes}}.

  • A probability of 0.50.5 (or 12\tfrac12) means the event is just as likely to happen as not.
  • The complement rule: P(not A)=1−P(A)P(\text{not }A)=1-P(A).

Worked Example: Drawing a Red Marble

Problem: A bag contains 5 red marbles and 7 blue marbles. What is the probability of drawing a red marble in one random pick?

  • Step 1: Identify totals. There are 5+7=125+7=12 marbles in all.
  • Step 2:
    P(red)=512P(\text{red})=\frac{5}{12}
    since 5 outcomes are favourable out of 12 equally likely outcomes.

By practising problems like this, you’ll grow confident in spotting favourable outcomes and calculating P(A)P(A). **Keep solving varied questions** to sharpen your exam skills!