Question

a large company states in its promotional literature that 74% of its employees have college degrees. assume this claim is true. if 3 employees are selected at random from this company, what is the probability that at least 1 of the selected employees will not have a college degree?
0.0176
0.4052
0.5948
0.9284

Explanation:

Step1: Calculate the probability that an employee has a college degree

Let \(p = 0.74\) (probability of having a college degree). Then the probability that an employee does not have a college degree is \(q=1 - p=1 - 0.74 = 0.26\)

Step2: Use the complement rule

The probability that at least 1 of the 3 employees does not have a college degree is \(P(X\geq1)\). The complement of \(P(X\geq1)\) is \(P(X = 0)\) (the probability that all 3 employees have a college degree).

Since the selections are independent, we use the formula for independent events \(P(A\cap B\cap C)=P(A)\times P(B)\times P(C)\)

\(P(X = 0)=p\times p\times p=(0.74)^3\)

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Step3: Calculate \(P(X\geq1)\)

Using the complement rule \(P(X\geq1)=1 - P(X = 0)\)

\(P(X\geq1)=1-0.405224 = 0.594776\approx0.5948\)

Answer:

0.5948