Hi all,
I came across this probability problem:
Let A1, A2, ..., An be events. Let Bk be the event that at least k of the Ai occur, and Ck be the event that exactly k of the Ai occur, for 0<=k<=n. Find a simple expression for P(Bk) in terms of P(Ck) and P(Ck+1).
My initial thought is that since we need to express P(Bk) in terms of P(Ck) and P(Ck+1), there must be some way to expression Bk in terms of Ck and Ck+1, but it seems P(Bk) should be equals to P(Ck) + P(Ck+1) + P(Ck+2) + ... + P(Cn), instead of just Ck and Ck+1, so I am stuck here, could any body provide some hint?
Thanks.
I came across this probability problem:
Let A1, A2, ..., An be events. Let Bk be the event that at least k of the Ai occur, and Ck be the event that exactly k of the Ai occur, for 0<=k<=n. Find a simple expression for P(Bk) in terms of P(Ck) and P(Ck+1).
My initial thought is that since we need to express P(Bk) in terms of P(Ck) and P(Ck+1), there must be some way to expression Bk in terms of Ck and Ck+1, but it seems P(Bk) should be equals to P(Ck) + P(Ck+1) + P(Ck+2) + ... + P(Cn), instead of just Ck and Ck+1, so I am stuck here, could any body provide some hint?
Thanks.