Four students place their phones on a desk. Later they each pick up a phone at random. What is the probability that exactly one student gets his/her phone?

- bahrom7893

- schrodinger

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- bahrom7893

@satellite73 can u help me out.

- anonymous

1/4

- bahrom7893

Arnab that's wrong. The probability that the first student gets his phone is 1/4th. What if the 2nd guy gets the phone. Then one phone is gone.

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## More answers

- bahrom7893

So the probability that second guy gets it is 1/3

- bahrom7893

ash, the answer's 1/3

- bahrom7893

idk how they got it though. Exactly one student gets the phone back.

- anonymous

100 % probability if they are in senses. lol
but it ll be 1/24

- anonymous

oh sorry, lemme think..

- anonymous

can someone please help me? x :)

- anonymous

yeah, it is coming 1/3 :)

- bahrom7893

I'm thinking:
(1/4) "first student got" + (2nd|Nobody else got theirs)

- bahrom7893

and then 3rd got his given nobody else got theirs and then 4th got his, etc..

- anonymous

first, pick up a phone at random and give it to the right person. it can be done in 4C1 ways= 4 ways.
rest of the 3 are to be deranged, so, D3= 2 ways.
so, the condition can be satisfied in total 4*2 ways=8 ways out of 4! ways= 24 ways.
so, the probability is 8/24=1/3

- anonymous

got it, @ bahrom7893?

- bahrom7893

what do u mean by deranged? this may be a dumb question, but I've never heard of the term before.

- anonymous

u know about derangement?

- bahrom7893

nope.

- anonymous

ok, derangement is a kind of arrangement where no right thing goes to right place..

- bahrom7893

Ohh ok. What is the formula for derangement?

- anonymous

http://en.wikipedia.org/wiki/Derangement

- anonymous

there is a general method:
Dr= r!(1/2!-1/3!+1/4!-..... upto 1/n!)

- Directrix

This problem is an updated version of the Secretary's Packet Problem
A secretary types four letters to four people and addresses the four envelopes. If she inserts the letters at random, each in a different envelope, what is the probability that exactly three letters will go into the right envelope?
http://www.cut-the-knot.org/Probability/IntuitiveProbability.shtml
Generalized here:
http://www.jstor.org/discover/10.2307/2690041?uid=3739616&uid=2129&uid=2&uid=70&uid=4&uid=3739256&sid=55851236913

- anonymous

sorry, last term is 1/r! ^^

- bahrom7893

kk ty everyone!

- anonymous

welcome :)

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