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.

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anonymous · Answer

since you are selecting "with replacement' the probability you get a defective one is the same on any trial, namely $.3$  i.e. the trials are independent
also there is only two possible outcomes, defective or not
therefore it is binomial