"Question 8
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 = mc2 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.
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 should have mentioned that on Mondays I lecture on calculus and I therefore always wear my jeans
(to make the lectures seem easier to understand). Find, on the basis of the complete information,
the probability that the photograph was taken on Sunday."
Hmm is this a question a joke do we think?