Grade 12 · Mathematics
Calculate probabilities of independent events
Independent events do not change each other’s probability. In Grade 12 Mathematics, the probability that two independent events both happen is P(A and B) = P(A) × P(B). Independence is an assumption that must be justified by the situation. Drawing without replacement usually changes the second probability, so the same shortcut cannot automatically be used.
Original explanation prepared with AI assistance.
Lees hierdie verduideliking in AfrikaansWhat you will practise
Identify independent events and calculate the probability that both occur.
The method
Identify the two events, confirm independence, and multiply their probabilities.
Worked example
A fair coin is tossed twice. What is the probability of two heads?
- Each toss has probability 1/2 of heads.
- The first toss does not affect the second.
- Multiply: P(two heads) = 1/2 × 1/2 = 1/4.
- The equally likely outcomes HH, HT, TH and TT confirm that one of four outcomes qualifies.
Common mistake
Add probabilities for suitable alternatives, but multiply for both independent events occurring.
Try it yourself
A fair die is rolled twice. Find the probability of a six on both rolls.
Show the explained solution
The rolls are independent: 1/6 × 1/6 = 1/36.
Curriculum and sources
Use the official CAPS subject document and your teacher’s annual plan to confirm the sequence and scope for your class. The link below is an official reference, not evidence of DBE approval of this explanation.
DBE: CAPS for the FET phaseFind your next lesson
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