A manufacturing machine has a 1% defect rate. If 10 items are chosen at random, what is the probability that at least one will have a defect?

probability (at least one defect is) is 0.096517 or 9.65 %

Explanation:

Given data

defect rate = 1%

no of sample = 10

to find out

probability at least one will have a defect

solution

we know here probability of defect is

Probability (defect) = 0.01

and n is 10

so

probability (at least one defect is) = 1 - probability (none) ... 1

we know probability (none) = 0.99^n

probability (none) = 0.99^10

put this in equation 1

probability (at least one defect is) = 1 - 0.99^10

probability (at least one defect is) is 0.096517 or 9.65 %