View Full Version : Struggling with a problem

04-21-2005, 02:31 PM
There are events A(1),A(2),A(3),....A(N) are independent. Suppose that:

P(A sub k) = 1/(k+1) For 1<=k<=n

Find the probability that none of the n events occur. This seems like an infinant tree of some sort and I am struggling to find a good starting point. Thanks in advance for any help.


04-21-2005, 03:10 PM
Independent means that P(A_i) does not depend on whether or not A_j occured... so find the probability that A_k does _not_ occur for all your ks (hint: it's 1 - P(A_k)) and multiply them all together.

So P(no A_k occuring) = (1/2)*(2/3)*...*(n/(n+1)) which turns out to be = (n!)/((n+1)!) = 1/(n+1)