Statistical and Discrete Mathematics
Core concepts
Understand discrete probability distributions, expected value, variance, and counting principles including permutations and combinations. Know the binomial distribution conditions and how to compute probabilities. Recognise when events are independent or mutually exclusive.
Traps
- Confusing permutations (order matters) with combinations (order does not).
- Assuming mutually exclusive events are independent; they are not, unless one has probability zero.
- Misidentifying binomial trials when trials are not independent or probabilities vary.
- Arithmetic slips in nCr and factorial cancellation.
Worked example
A fair coin is tossed 5 times; find the probability of exactly 2 heads. Using the binomial with n=5, p=0.5: C(5,2)(0.5)^2(0.5)^3=10/32=5/16.
Rule of thumb
Ask whether order matters before choosing between permutations and combinations; then confirm the binomial conditions of fixed trials, independence, and constant probability.