You are Here: Home >< Maths

# Maths Help - Algebra. watch

1. 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.
2. 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?
3. 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'.
4. just work out how many different probabilties there are.

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

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

Then:
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.
Understand?
5. Take into account 1/10 glasses being faulty too.

been awhile since I did stats, it sucks balls
6. Sorry, I haven't been on my computer since I posted.

It's binomial. That's the full question written in the OP.
7. OK then use standard binomial formula to calculate p(none faulty) and p(exactly one faulty) in the first box.

### Related university courses

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: January 17, 2010
Today on TSR

How do you think you'll do?

### University open days

Wed, 25 Jul '18
2. University of Buckingham
Wed, 25 Jul '18
3. Bournemouth University
Wed, 1 Aug '18
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams