A corporation has 10 manufacturing plants. Of these, seven are domestic and three are outside of the country. Each year a performance evaluation is conducted for four randomly selected plants. What is the probability that a performance evaluation will include at least one plant outside of the country? (Hint: Begin by finding the probability that only domestic plants are selected.)

The probability that a performance evaluation will include at least one plant outside of the country is 0.76.

Step-by-step explanation:

The random variable X can be defined as the number of outside of the country plants that are selected for a performance evaluation.

A sample of n = 4 plants are selected each year for a performance evaluation.

The probability of selecting an outside of the country plant is, p = 0.30.

A plant selected can either be a domestic plant or outside of the country plant. They are not dependent on each other.

Thus, the random variable X follows a Binomial distribution with parameters n = 4 and p = 0.30.

The probability mass function of X is:

Compute the probability that a performance evaluation will include at least one plant outside of the country as follows:

P (X ≥ 1) = 1 - P (X < 1)

             = 1 - P (X = 0)

Thus, the probability that a performance evaluation will include at least one plant outside of the country is 0.76.

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