80% of the items produced are non-defective. if three items are examined, what is the probability that at most one is non- defective? use the binomial probability function to answer this question.

Binomial distribution can be used because the situation satisfies all the following conditions:
1. Number of trials is known and remains constant (n)
2. Each trial is Bernoulli (i.e. exactly two possible outcomes) (success/failure)
3. Probability is known and remains constant throughout the trials (p)
4. All trials are random and independent of the others
The number of successes, x, is then given by

where


Here given
p=0.8   (success=non-defective)
n=3
x=0 or 1
Then







probability of at most one non-defective out of a random sample of three is 0.104

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since the cosine is the ratio of the adjacent side to the hypotenuse, you can see that cos 60° = ½. answer. according to the property of cofunctions (topic 3), sin 30° is equal to cos 60°. sin 30° = ½.