A telephone survey uses a random digit dialing machine to call subjects. The random digit dialing machine is expected to reach a live person 25% of the time. What is the probability (rounded to two decimal places) that no calls are successful in ten attempts?

5.63% probability (rounded to two decimal places) that no calls are successful in ten attempts

Step-by-step explanation:

For each call, there are only two possible outcomes. Either they are succesful, or they are not. The probability of a call being sucessful is independent of other calls. So we use the binomial probability distribution 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.

In which is the number of different combinations of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.

The random digit dialing machine is expected to reach a live person 25% of the time.

This means that

What is the probability (rounded to two decimal places) that no calls are successful in ten attempts?

This is P(X = 0) when n = 10. So

5.63% probability (rounded to two decimal places) that no calls are successful in ten attempts

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step-by-step explanation: