Probability question：
An experiment has three possible outcomes A, B and C with respective probabilities p, q and r, where p+q+r=1. The experiment is repeated until either outcome A or outcome B occurs. Show that A occurs before B with probability p/(p+q).

Question

Probability question：
An experiment has three possible outcomes  A,  B and  C with respective probabilities  p,  q and  r, where  p+q+r=1. The experiment is repeated until either outcome  A or outcome  B occurs. Show that  A occurs before  B with probability  p/(p+q).

shubhamsrg · Answer

your favorable cases are
A occurs in first trial
C occurs in first trial and then A occurs in 2nd.
C occurs in 1st and 2nd trial, and then A in 3rd. 
and so on..

so required probability is :
p + rp + r^2 p + r^3 p ...

you should be able to simplify it from here on.
note that 0<p,q,r<1 

hope this helps

amistre64 · Answer

sounds like a trinomial distribution ....

anonymous · Answer

sorry for that. mistake