there are 4 boys and a list of 4 songs, every boy is randomly picked to sing a one song.
What is the probability that the 3rd boy will sing the 4th song?

$|\Omega|=4! $, event $A=${_ _ _ 3rd} there are $3!$ option left so it is $\frac{3!}{4!}=\frac{1}{4}$ and intuitively it is $\frac{1}{4}$ too.

I am trying to solve it using conditional probability, I was given the following tree ($L_i$=the 3rd boy sings the i-th song)

enter image description here

How should I approach it (without the tree)?


1 Answer 1


It is $1/4$, because here the ordering does not matter at all, it's all just someone choosing one song over four possible.

(Unless the song is Wonderwall, of course. Then it is more likely to be chosen.)

  • $\begingroup$ added more info about my question $\endgroup$
    – gbox
    Jul 8, 2015 at 14:25

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