Conditional probability P(A|B), independent events, possibility space diagrams, tree diagrams limited to two initial branches, and Venn diagrams for solving problems.
5 narrated scenes. Press play, listen and read along — the points appear as they are explained. Use ‹ Prev / Next › or the scene bar to jump to any scene.
“Given that it rained, what is the chance he was late?” Conditional probability answers questions where you already know part of the story.
Narration uses your device’s built-in voice. No sound? Switch to “Captions only” — the captions advance on their own.
Copy these into your notebook in your own words — that is how they stick.
P(A | B) = P(A ∩ B)/P(B), P(B) ≠ 0.
P(A ∩ B) = P(A)P(B) ⇔ P(A | B) = P(A).
P(A ∩ B) = 0 — cannot be independent if both have positive probability.
Multiply along branches; add branches for an event; branches from a node sum to 1.
Use the tree: P(A | B) = (branch for A and B)/(total for B).
List/grid all equally likely outcomes; restrict to the given condition.
Up to two sets: fill from the intersection outwards.
probability × number of trials.
3 quick games on this lesson. Earn XP and badges as you play — your best score for each game is saved. Games are for practice and do not change your exam readiness. More games in the Additional Mathematics Arcade.
8 items modelled on real CSEC Paper 1 questions. Choose one answer for each, then check. Aim for 80% or better. Work each item on paper first.
Write full answers, then reveal the mark scheme and tick the points you earned (22 marks in total). Show all your working — method marks count. Your answers are saved on this device.
Question 1 [11 marks]
P(A) = 0.7, P(B) = 0.4 and P(A ∩ B) = 0.3.
(a) Find P(A | B) and P(B | A). [4]
(b) Determine whether A and B are independent. Give a reason. [3]
(c) Find P(A′ ∩ B′). [2]
(d) Explain why A and B cannot be mutually exclusive. [2]
Question 2 [11 marks]
The probability that it rains on a school day is 0.3. If it rains the probability that Sam is late is 0.5; if it does not rain the probability that he is late is 0.1.
(a) Draw a tree diagram showing all the probabilities. (Check: two first branches 0.3 and 0.7; second branches 0.5, 0.5 and 0.1, 0.9; outcomes labelled.) [3]
(b) Find the probability that Sam is late. [3]
(c) Given that Sam is late, find the probability that it rained. [3]
(d) In a term of 40 school days, how many days would you expect Sam to be late? [2]
Find these in your own past-paper booklets for extra timed practice. Items above are written in the style of these papers; any adapted from a specific question say so.