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## #1 2009-03-31 08:33:54

Daniel123
Member
Registered: 2007-05-23
Posts: 663

### Probability

Each day I choose at random between my brown trousers, my grey trousers and my expensive but fashionable designer jeans. Also in my wardrobe, I have a black silk tie, a rather smart brown and fawn polka-dot tie, my regimental tie, and an elegant powder-blue cravat which I was given for Christmas. With my brown or grey trousers, I choose ties (including the cravat) at random, except of course that I don't wear the cravat with the brown trousers or the polka-dot tie with the grey trousers. With the jeans, the choice depends on whether it is Sunday or one of the six weekdays: on weekdays, half the time I wear a cream-coloured sweat-shirt with E=mc^2 on the front and no tie, otherwise, and on Sundays (when naturally I always wear a tie), I just pick at random from my four ties.

a) This morning, I received through the post a compromising photograph of myself. I often receive such photographs and they are equally likely to have been taken on any day of the week. However in this particular photograph, I am wearing my black silk tie. Show that, on the basis of this information, the probability that the photograph was taken on Sunday is 11/68.

I get 3/14, and I can't see where I've gone wrong. Can anyone confirm the question's answer?

Thanks

(I appreciate it's long, but it's pretty straightforward and shouldn't take long)

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## #2 2009-03-31 09:07:18

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: Probability

Why did the vector cross the road?
It wanted to be normal.

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## #3 2009-03-31 09:26:52

Daniel123
Member
Registered: 2007-05-23
Posts: 663

### Re: Probability

ARGH. I misread the question. I thought the E=mc^2 sweat-shirt can be worn on all weekdays, regardless of the trousers.

Thanks mathsy.

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