1. Does selecting people without replacement always give independent trials?
- Yes
- No
- Only if n is even
Check the answer and reasoning
No
Removing a person can change later selection probabilities.
MATH / AS level
Statistics option: distributions
Permutations count ordered arrangements; combinations count selections. Discrete distributions assign probabilities to numerical outcomes and allow expectations to be calculated.
Learning objectives
- Explain statistics option: distributions using a concrete example.
- Apply the worked method and justify each step.
- Recognise the limitation described in the final check.
The big idea
Permutations count ordered arrangements; combinations count selections. Discrete distributions assign probabilities to numerical outcomes and allow expectations to be calculated.
A binomial model needs fixed n, independent trials and a constant success probability. A normal model is continuous and symmetric; standardisation measures distance from the mean in standard deviations.
Equations and relationships
Expected number of successes.
Worked example
X~B(10,0.3). Find E(X).
Follow the solution
Multiply n by p: 10×0.3=3; an expectation need not be an observed outcome.
Investigate and explain
Predict the worked result before calculating. Change one input, record the new result, and explain which assumptions still hold.
Related interactive model. Compare its assumptions with the explanation; it is not a complete syllabus lesson.
Check your understanding
2. X~B(10,0.3). Find E(X).
- 0.3
- 7
- 3
Check the answer and reasoning
3
Multiply n by p: 10×0.3=3; an expectation need not be an observed outcome.
3. For a normal distribution, what proportion is below its mean?
- 1/2
- 1/4
- 1
Check the answer and reasoning
1/2
Symmetry places half the probability on each side of the mean.