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    • Thread Starter

    It is known that 1 in 10 drinking glasses produced from a production line are faulty. They are packed in boxes of 6 and a batch of glasses contains a large number of these boxes.

    A quality control inspector tests each batch as follows:
    - He chooses a box at random and inspects the glasses
    - If none are faulty then the whole batch is inspected.
    - If one is faulty, then he chooses a second box and accepts the whole batch if only the box contains at most one faulty glass.
    - Otherwise, he rejects the whole batch.

    Find the probability that the batch is rejected.

    How can this be solved? Thanks.

    Just started to look at this - it feels like an S1 A level question - could you confirm 'if none are faulty then the whole batch is inspected - are you sure it's not accepted ?

    Have you learned the use of binomial theorem for problems like this or are you expecting to draw a large tree?

    It is going to be a binomial distribution problem.

    As it stands, it has no solution, as we don't know the accept/reject criteria for when 'the whole batch is inspected'.

    just work out how many different probabilties there are.

    So every batch, he takes a glass from a boxand checks it.

    Glass is fine, accepts the batch
    Glass is faulty - checks another box

    All are fine: Batch accepted
    1 is broken: Batch accepted
    2 are broken: Batch denied
    3 are broken, batch denied
    4 are broken, batch denied
    5 are broken, batch denied
    6 are broken, batch denied.

    so, eight possible outcomes, 3 of which the batch is accepted, 5 are denied

    I make that a 3/5 chance of the batch being accpeted.

    Take into account 1/10 glasses being faulty too.

    been awhile since I did stats, it sucks balls
    • Thread Starter

    Sorry, I haven't been on my computer since I posted.

    It's binomial. That's the full question written in the OP.

    OK then use standard binomial formula to calculate p(none faulty) and p(exactly one faulty) in the first box.
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