A manufacturer of compact-disk players subjects the equipment to a comprehensive testing process for all mechanical and electrical functions before the equipment leave the factory. Ideally, the hope is that each compact-disk player passes on the first test. Suppose that past data indicate that the probability that a compact-disk player passes the first test is 0.9. If 4 compact-disk players are randomly selected, determine the probability for Question a-f and round your answer to four decimal places.

For each disk, there are only two possible outcomes. Either it passes the first test, or it does not. The probability of a disk passing the first test is independent of any other disk. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Suppose that past data indicate that the probability that a compact-disk player passes the first test is 0.9.

This means that [tex]p = 0.9[/tex]

4 compact-disk players are randomly selected

This means that [tex]n = 4[/tex]