Respuesta :
Answer:
There is a 33.67% probability that exactly one of them is defective.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
Here, we can have different formats. For example, D-ND-ND is the same as ND-D-ND, that is, the ordering is not important. So we use the combinations formula.
Combinations formula:
[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]
Desired outcomes
One defective(one from a set of 55) and two non defective(two from a set of 45). So
[tex]D = C_{55,1}*C_{45,2} = \frac{55!}{54!1}*\frac{45!}{43!2!} = 55*45*22 = 54450[/tex]
Total outcomes
Three from a set of 100. So
[tex]T = C_{100,3} = \frac{100!}{97!3!} = 161700[/tex]
What is the probability that exactly one of them is defective
[tex]P = \frac{D}{T} = \frac{54450}{161700} = 0.3367[/tex]
There is a 33.67% probability that exactly one of them is defective.
