Hi people! I'm new to probability and so while going through conditional probability I found the following problem which I solved by arguing directly without using any results of Conditional Probability ............unfortunately the answer wasn't given. The problem goes as:
There are 4 friends A,B,C, D and a referee. A puts a '+' or a '-' sign on a piece of paper and passes it to B who perhaps changes the sign and passes the slip to C, who may change the sign and passes it to D. D perhaps changes the sign and finally passes the slip to the referee. Suppose 2/3 is the prob. of writing a '+' by A and each of B,C,D changes the sign by prob 1/3 independently. If the referee notices a '+' sign on the slip, then find the prob that A wrote a '+' on the slip.
I would really appreciate if someone gave me the solution. Also assuming the same conditions, what would then be the ans, instead of 4 friends if n friends did the same thing.