Mutually exclusive and independent events, the addition and multiplication rules, tree diagrams with and without replacement, contingency tables and experimental probability.
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.
“What is the probability of at least one head in three tosses?” “Two red balls without replacement?” Two rules and a tree diagram answer them all.
Narration uses your device’s built-in voice. No sound? Switch to “Captions only” — the captions advance on their own.
Roll a die many times and compare with the theoretical probability.
Copy these into your notebook in your own words — that is how they stick.
Cannot happen together: P(A or B) = P(A) + P(B).
P(A or B) = P(A) + P(B) − P(A and B).
One does not affect the other: P(A and B) = P(A) × P(B).
1 − P(none).
Multiply along branches; add paths. Branches from one point sum to 1.
Probabilities change after the first draw (denominator decreases).
Probability = cell ÷ grand total; check the table adds up.
Relative frequency = successes ÷ trials; approaches theoretical value with more 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 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 (18 marks in total). Show all your working — method marks count. Your answers are saved on this device.
Question 1 [9 marks]
A bag contains 5 red balls and 3 blue balls. Two balls are drawn at random, one after the other.
(a) The first ball is replaced before the second is drawn. Calculate the probability that (i) both balls are red, (ii) the balls are different colours. [4]
(b) The first ball is NOT replaced. Calculate the probability that (i) both balls are red, (ii) the second ball is blue. [5]
Question 2 [9 marks]
The table shows how 40 students travel to school. Boys: 12 by bus, 6 by car; girls: 14 by bus, 8 by car.
(a) Complete the contingency table with totals. [2]
(b) A student is chosen at random. Find the probability that the student (i) travels by bus, (ii) is a girl who travels by car. [3]
(c) A fair die is rolled and a fair coin is tossed. Find the probability of an even number and a tail. [2]
(d) Two events A and B are mutually exclusive with P(A) = 0.35 and P(B) = 0.45. Find P(A or B) and P(neither A nor B). [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.