a large company states in its promotional literature that 74% of its employees have college degrees. assume…

a large company states in its promotional literature that 74% of its employees have college degrees. assume this claim is true. if 4 employees are selected at random from this company, what is the probability that at least 1 of the selected employees has a college degree?\n0.0046\n0.2999\n0.7001\n0.9954

a large company states in its promotional literature that 74% of its employees have college degrees. assume this claim is true. if 4 employees are selected at random from this company, what is the probability that at least 1 of the selected employees has a college degree?\n0.0046\n0.2999\n0.7001\n0.9954

Answer

Explanation:

Step1: Find probability of no - college - degree

The probability that an employee does not have a college degree is $1 - 0.74=0.26$.

Step2: Find probability that none of 4 have college degrees

Since the selections are independent, the probability that none of the 4 selected employees have college degrees is $(0.26)^4$. $(0.26)^4=0.26\times0.26\times0.26\times0.26 = 0.00456976\approx0.0046$.

Step3: Find probability that at least 1 has a college degree

The probability that at least 1 of the 4 selected employees has a college degree is the complement of the event that none of them have a college degree. Let $P(X\geq1)$ be the probability that at least 1 has a college degree. Then $P(X\geq1)=1 - P(X = 0)$. $P(X\geq1)=1-(0.26)^4=1 - 0.0046 = 0.9954$.

Answer:

0.9954