Probability & distributions

The topic on one screen

• Mutually exclusive means $P(A\cap B)=0$. Independent means $P(A\cap B)=P(A)P(B)$, equivalently $P(A\mid B)=P(A)$ when the conditional probability is defined. They are different ideas.
• Conditional probability reverses the reference group: $P(A\mid B)=\dfrac{P(A\cap B)}{P(B)}$. A tree, Venn diagram or two-way table is often the safest way to identify the numerator and denominator.
• A binomial model $X\sim B(n,p)$ needs a fixed number of trials, two outcomes per trial, constant success probability and independent trials. State which assumption is doubtful when you critique the model.
• For $X\sim B(n,p)$, distinguish $P(X=r)$, $P(X\leq r)$ and $P(X\geq r)=1-P(X\leq r-1)$. The most common calculator error is an off-by-one complement.
• A Normal model $X\sim N(\mu,\sigma^2)$ is continuous and symmetric. Standardise with $Z=\dfrac{X-\mu}{\sigma}$; the second parameter is the variance, even when the question gives a standard deviation.
• A model is useful only if its assumptions fit the context. Independence, constant $p$, symmetry and an unrestricted Normal range are modelling decisions, not facts supplied by the calculator.

Where students actually lose marks

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Questions are written in the style of past Edexcel papers (source shown on each) — never copied from them.

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