Probability and Statistics
Core concepts
You must handle discrete and continuous probability, conditional probability, independence, and the binomial and normal distributions. Key rules include the addition rule P(A ∪ B) = P(A) + P(B) − P(A ∩ B), the multiplication rule for independent events, and conditional probability P(A|B) = P(A ∩ B)/P(B).
For the binomial distribution, identify n trials, constant probability p, and independent outcomes; the mean is np and the variance is np(1 − p). For the normal distribution, standardise using z = (x − μ)/σ and use symmetry and tables. Descriptive statistics, including mean, median, standard deviation, and the effect of outliers, also appear.
Traps to watch
- Confusing P(A|B) with P(B|A).
- Assuming independence when it is not stated.
- Forgetting the continuity correction when approximating a discrete distribution with a normal one.
- Using population standard deviation formulas when the data are a sample.
Rule of thumb
Draw a tree diagram or Venn diagram before computing. Check whether events are independent by testing P(A ∩ B) = P(A)P(B) rather than assuming it.
Worked example
A bag has 3 red and 5 blue balls; two are drawn without replacement. The probability both are red is (3/8)(2/7) = 6/56 = 3/28. Because the first draw changes the composition, the events are not independent, so the simple product of marginal probabilities would be wrong.