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.
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- Thread Starter
- 15-01-2010 07:24
- 15-01-2010 08:42
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?
- 15-01-2010 09:51
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'.
- 15-01-2010 10:03
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.
- 15-01-2010 10:08
Take into account 1/10 glasses being faulty too.
been awhile since I did stats, it sucks balls
- Thread Starter
- 16-01-2010 15:52
Sorry, I haven't been on my computer since I posted.
It's binomial. That's the full question written in the OP.
- 17-01-2010 18:04
OK then use standard binomial formula to calculate p(none faulty) and p(exactly one faulty) in the first box.