How much does a package containing a dress weigh?

What is the probability that a person will buy a package containing at least one fault product given the situation in the details section?

• Assumingly, there is a contact lens manufacturing machine of which has 1% producing defected contact lens. In a week, this machine will produce approximately 10000 contact lens which will be bundled as 6-lens packages (A packaging machine will randomly select 6 each time from 10000 products). Weekly, What is the probability that a person will buy a package containing at least one fault product?.

• Answer:

  Edit - I just reread the question and should clarify that I am answering for "at least one person," not "a given person." If you meant "a given person" the answer is different and the box of 6 lens is of course relevant. The approach to the problem is still the same. This looks like homework, so I'll just get you started... The probability of at least one defect is 1 minus the probability that everybody gets a perfect product. The package of 6 lens is irrelevant - 1 person opening a box of 6 perfect lens is the same as 6 people opening a box of 1 perfect lens. The probability of producing a perfect lens is 1 minus the probability of a defect. Lens production is likely assumed independent for this problem, so the probability of multiple events is the probability of each individual event multiplied together. This should be more than enough to get the exact answer. I came up with: it is almost certain that at least one person will receive a defective lens. Think about it - a 1 in 100 chance, 10,000 times. Yikes. For a given person, it's not so bad. A 1 in 100 chance 6 times. It's obviously not 6/100, but the answer is pretty close to that.