A box contains 10 items, of which 3 are defective and 7 are 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

https://onlinecourses.science.psu.edu/stat200/node/37

Note in particular:

For a variable to be a binomial random variable, ALL of the following conditions must be met:

* There are a fixed number of trials (a fixed sample size)
* The probability of a success is the same on each trial
* Trials are independent of one another