Respuesta :
Answer:
0.0645 = 6.45% probability that exactly 10 employees will be tested in order to find 3 positives
Step-by-step explanation:
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
40% of the employees have positive indications of asbestos in their lungs
This means that [tex]p = 0.4[/tex]
a) Find the probability that exactly 10 employees will be tested in order to find 3 positives
2 within the first 9([tex]P(X = 2)[/tex] when [tex]n = 9[/tex]), and the 10th, with 0.4 probability. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{9,2}.(0.4)^{2}.(0.6)^{7} = 0.1612[/tex]
0.4*0.1612 = 0.0645
0.0645 = 6.45% probability that exactly 10 employees will be tested in order to find 3 positives
