Dear Allstat members,
The following probability problem was given to me by a colleague who
wishes to be nameless. I tried without success to solve it
during a train journey. My approximate answer is at the end, but I
welcome an accurate answer from anyone.
Regards
Miland Joshi
The problem:
Have one pack of cards (shuffled), ask a person to name any two types
of card, eg. jack and two (suits not included). Then just go
through the pack of cards placing the cards face up on the table and
aparently there's a good chance that these cards will turn up next to
each other.
Is this true???
(My approximate answer is:
Suppose the numbers specified are different, say 7
and 3. Suppose for simplicity that apart from the four 3's, of the 48
cards laid out the 7s are not at the ends, and have at least two
spaces between them. Then there are 49 possible 'slots' in which the
3's can go, and of these 8 will result in a 7 and a 3 being next to
each other. Hence the probability that this will not happen is
((41/49)^4) = 0.49. Hence, bearing in mind the simplifications, the
chance that we will get a 3 and a 7 together is about even]
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