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The probability that at least 1 of the selected employees will not have a college degree is 0.594776.
What is Binomial distribution?
A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. It is given by the formula,
[tex]P(x) = ^nC_x p^xq^{(n-x)}[/tex]
Where,
- x is the number of successes needed,
- n is the number of trials or sample size,
- p is the probability of a single success, and
- q is the probability of a single failure.
Given that 74% of the employees have degrees, therefore, 26% of the employees have no degree.
Now, since we want at least any one of the three people selected to have a degree. Therefore, the probability of everyone having a degree can be written as,
Probability that at least any one of the three people selected to have a degree = 1 - Probability of everyone having a degree
Now, using the binomial distribution we can write,
[tex]\text{Probability} = 1 - [^3C_0\cdot(0.26)^0 \cdot (0.74)^{(3-0)}]\\\\\text{Probability} = 1 - 0.405224 = 0.594776[/tex]
Hence, the probability that at least 1 of the selected employees will not have a college degree is 0.594776.
Learn more about Binomial Distribution:
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