A corporation has 11 manufacturing plants. Of these, seven are domestic and four are outside the United States. 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 the United States

The probability that a performance evaluation will include at least one plant outside the United States is 0.836.

Step-by-step explanation:

Total plants = 11

Domestic plants = 7

Outside the US plants = 4

Suppose X is the number of plants outside the US which are selected for the performance evaluation. We need to compute the probability that at least 1 out of the 4 plants selected are outside the United States i. e. P (X≥1). To compute this, we will use the binomial distribution formula:

P (X=x) = ⁿCₓ pˣ qⁿ⁻ˣ

where n = total no. of trials

x = no. of successful trials

p = probability of success

q = probability of failure

Here we have n=4, p=4/11 and q=7/11

P (X≥1) = 1 - P (X<1)

= 1 - P (X=0)

= 1 - ⁴C₀ * (4/11) ⁰ * (7/11) ⁴⁻⁰

= 1 - 0.16399

P (X≥1) = 0.836

The probability that a performance evaluation will include at least one plant outside the United States is 0.836.