Expected number of successes: For X ~ B(n, p) the mean (expected number of successes) is E(X) = np — just trials × success probability.
IB-style question — the mean
X ~ B(50, 0.2).
Find the expected number of successes.
Step by step
- Mean = np.
- Evaluate.
Final answer
E(X) = 10.
This is the 'expected number': A 'how many do you expect to…' binomial question is just np.
Free preview
This is the free notes preview
You're reading the free notes. Aimnova Pro unlocks the full study experience — and you can try it free for 7 days:
- FlashcardsLock in vocabulary and key terms with spaced repetition.
- Practice questionsAnswer exam-style questions and get instant AI marking.
- Mock exams & past-paper vaultSit full mocks and see exactly how examiners award marks.
- Personalised study planA daily plan built around your exam date and weak areas.
Start your 7-day free trial Full access to Aimnova Pro · cancel anytime
Spread of the binomial: The variance is Var(X) = np(1 − p), and the standard deviation is its square root, √(np(1−p)).
IB-style question — variance & sd
X ~ B(50, 0.2).
Find the variance and standard deviation.
Step by step
- Variance = np(1 − p).
- Standard deviation = √variance.
Final answer
Variance = 8; standard deviation ≈ 2.83.
Use (1 − p), not p, twice: Variance is np(1 − p) — multiply by both p and (1 − p); a common slip is np² or n p.
Practice with real exam questions
Answer exam-style questions and get AI feedback that shows you exactly what examiners want to see in a full-marks response.
Try Practice Free7-day free trial • No card required
Use mean and variance together to find n and p: Given the mean np and variance np(1−p), divide them: variance ÷ mean = (1 − p), which gives p; then n = mean ÷ p.
IB-style question — find n and p
A binomial variable has mean 24 and variance 14.4.
Find n and p.
Step by step
- variance ÷ mean = (1 − p).
- n = mean ÷ p.
Final answer
p = 0.4 and n = 60.
Divide to remove n: Dividing variance by mean cancels n, leaving (1 − p) — a clean way in.