Question

A box contains 10 items, of which 3 are defective and 7are non defective. Two items are randomly selected, one at a time, with replacement, and x is the number of defectives in the sample of two. Explain why x is a binomial random variable

Answer 1

Necessary and sufficient conditions for application of binomial distribution :
1. trial must be Bernoulli, i.e. exactly two outcomes (defective or not defective)
2. number of trails is known and not dependent on outcomes (2).
3. probability of each trial must be known and is constant throughout trials (3/10, with replacement)
4. all trials are random and independent of each other.