Mastering Mathematics Smartly
by Wee Wen Shih

Determining the distribution

To determine if a random variable follows a Binomial distribution (when it is not obvious from the problem description), you need to identify, from the given question, two pieces of information: 

(1) n (i.e. the number of items selected at random),

(2) p (i.e. the probability of a successful outcome).

To determine if a random variable follows a Poisson distribution (when it is not obvious from the problem description), you need to identify keywords such as "average rate", "mean" and the like.

Types of two-scenario probability questions

(1) Poisson in the first scenario, then Binomial in the second scenario.
See example.

(2) Binomial in the first scenario, then Binomial in the second scenario.
See example.

(3) Poisson in the first scenario, then Poisson in the second scenario.
See example.

(4) Questions that require a suitable approximation (which have been elaborated in Poisson-Binomial approx, Normal-Poisson approx, Normal-Binomial approx).

Try these!