Answer:
There is a 44.16% probability that exactly 1 of the tested bottles is contaminated.
Step-by-step explanation:
[tex]C_{n,x}[/tex] is the number of different combinatios of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem, we have that:
Total number of combinations:
[tex]C_{22,3} = \frac{22!}{3!(18)!} = 1540[/tex]
Desired combinations:
It is 1 one 5(contamined) and 2 of 17(non contamined). So:
[tex]C_{5,1}*C_{17,2} = 5*17*8 = 680[/tex]
What is the probability that exactly 1 of the tested bottles is contaminated?
[tex]P = \frac{680}{1540} = 0.4416[/tex]
There is a 44.16% probability that exactly 1 of the tested bottles is contaminated.
