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.

Question

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For the first question about the box containing 10 items of which 3 are defective, what is the probability of any one selected item being non-defective?
X

Answer 1

There are n specified ‘trials’.

Each observation results in one of two possible outcomes, called ‘success’ and ‘failure’.

The probability of a ‘success’ remains the same from one trial to the next.

The outcomes are independent from one trial to the next

7/10 = 0.7