Math Is Fun Forum

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)

I ended up having to do this by finding a reduction formula for

Is there another way?

Thanks.

I have a pair of simultaneous equations. The solution I have solves them by 'inspection'. Fair enough. Why can't I solve them by substitution? I can't get it to work.

The solution says "by inspection, A = - 2, B = 0". When I use substitution, I can't get these answers.

Thanks.

100 floor tower. 2 identical plates. How many times do we have to drop a plate to find the minimum floor from which dropping a plate will cause it to smash?