30 January
2015
Puzzle from India
I was enroute from India to USA when I got a call from one of my nephews with the following math problem he was stuck with. I am posting that as the puzzle of this week.
There is a jar with 50 pieces of paper written “1” thru “50” in them. You pick 5 of them at random and lay them out in increasing sequence. What is the probability that the middle number is 30?
Kon class ey nephew? :@
1 out of 50 (from Steve)
1
Class X
i was going to say 0.036408 but this says “Puzzle from India” so there must be a catch. đŸ™‚
There is no catch. That is the answer. Deepak, yours is the same too.
29c2 x 20c2 / 50c5 ?
Yeah
Do you think that standard of Indian schools are at par with that of U.S.A?
# of ways of choosing 5 numbers from a pack of 50 = 50C5
So, this is our universal set.
Desirable pattern = A < B < 30 < C < D
There are 29 numbers smaller than 30. Choosing two (A and B) from them = 29C2
There are 20 numbers larger than 30. Choosing two (C and D) from them = 20C2
Therefore, the required probability = 29C2.20C2/50C5
I have not thought about this problem in some time but my first guess was exactly the way you figured out. Total possibilities 50C5. Favorable cases has to have a 30 and then 2 from one set of 20 numbers and 2 from one set of 29 numbers…