Grade 12 · Mathematics
Probability
Use complements, the addition rule and independence to solve probability questions.
Union and intersection
A union means A or B, including both. An intersection means both A and B. Subtract the intersection once in the addition rule to avoid counting it twice.
Independence
Events are independent when knowing one occurred does not change the probability of the other. For independent events, multiply their probabilities to find the intersection.
Formula sheet
- P(not A) = 1 - P(A)
- P(A or B) = P(A) + P(B) - P(A and B)
- If independent: P(A and B) = P(A) × P(B)
Worked example
A fair die is rolled. A is an even number; B is a number greater than 4. Find P(A or B).
- A = {2, 4, 6}; B = {5, 6}.
- P(A) = 3/6, P(B) = 2/6 and P(A and B) = 1/6.
- P(A or B) = 3/6 + 2/6 - 1/6 = 4/6 = 2/3.
Try it yourself
1. P(A) = 0.4. Find P(not A). Check answer
1 - 0.4 = 0.6.
2. Independent events have probabilities 0.3 and 0.5. Find the probability of both. Check answer
0.3 × 0.5 = 0.15.
Common mistake: Mutually exclusive events and independent events mean different things.