The data mentioned in the question can be expressed as PB=0.25, PW=0.25, PS=0.50, PGB=0.40, PGS=0.20, and PGW=0.10. The probability that a stock rated a good buy by the analyst performed much better than the average, can be expressed as PBG. By using the Baye's theorem, the probability PBG can be given as PBG=PB·PGBPB·PGB+PW·PGW+PS·PGS. PBG=PB·PGBPB·PGB+PW·PGW+PS·PGS=0.25·0.400.25·0.40+0.25·0.10+0.50·0.20≈0.444 Therefore, the probability that a stock rated a good buy by the analyst performed much better than the average, is approximately 0.444
When I calculate these numbers I get 0.135, and I'm not sure how you get .444?
I think I need a little clarification.
Thank you.
The data mentioned in the question can be expressed as PB=0.25, PW=0.25, PS=0.50, PGB=0.40, PGS=0.20, and PGW=0.10.
The probability that a stock rated a good buy by the analyst performed much better than the average, can be expressed as PBG.
By using the Baye's theorem, the probability PBG can be given as PBG=PB·PGBPB·PGB+PW·PGW+PS·PGS.
PBG=PB·PGBPB·PGB+PW·PGW+PS·PGS=0.25·0.400.25·0.40+0.25·0.10+0.50·0.20≈0.444
Therefore, the probability that a stock rated a good buy by the analyst performed much better than the average, is approximately 0.444.
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