Respuesta :
Answer:
78.46% probability that at least one of the calculators is defective
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
The order that the calculators are chosen is not important. So we use the combinations formula to solve this problem.
Combinations formula:
The number of combinations of x elements from a set of n elements is given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
What is the probability that at least one of the calculators is defective?
Either none of them are defective, or at least one is. The sum of these probabilities is 100%.
So
ND + A1D = 100
A1D = 100 - ND
In which ND is the probability that none are defective.
Probability that none are defective
Desired outcomes:
40 calculators have no defects, and 4 are going to be chosen
[tex]D = C_{40,4} = \frac{40!}{4!36!} = 91390[/tex]
Total outcomes:
58 calculators in total, and 4 are going to be chosen
[tex]T = C_{58,4} = \frac{58!}{4!54!} = 424270[/tex]
Probability:
[tex]P = \frac{91390}{424270} = 0.2154[/tex]
21.54% probability that no calculators are defective, so ND = 21.54.
At least one defective:
A1D = 100 - ND = 100 - 21.54 = 78.46
78.46% probability that at least one of the calculators is defective
