# HELP with PROBABILITY QUESTION

This is in the Volume 1 of the Schweser exam book, Exam 1, morning section quest. 28 Alex White, the current portfolio manager, is examining his portfolio. The portfolio contains 100 stocks that are either value or growth stocks. 40% of the stocks are value stocks. A previous port manager selected 70% of the value stocks and 80% of the growth stocks. What is the probability of selecting a stock at random that is either a value stock or was selected by a previous manager? ANSWER 88% In setting up the probabilities, i set up the equation P(A or B) = P(A) + P(B)-P(AB). P(A)= the probability of selecting a random variable that is a value stock. I understand how we get P(A) which is given to be .40, and then I got P(B) - probability of selecting a stock that was picked by a previous manager, which is the sum of all the conditional probabilities to get the unconditional probability of P(B). But what I don’t understand is why do we use P(A) times P(B) to get the probability of P(AB)? because these are DEPENDENT EVENTS, so shouldn’t the P(AB)=P(A|B)*P(B)? instead of the joint probability for INDEPENDENT events P(A)*P(B)=(PAB)? Also does anyone know of any book that could help with probabilities concepts or videos? I seem to NEVER get the probabilities questions right If you have the time, watch this guy’s explanation. It works for me, that is. http://www.youtube.com/watch?v=3ER8OkqBdpE&feature=PlayList&p=C58778F28211FA19&index=0

100 stocks total. 40 are Value 60 are Growth. The previous manager selected 70% of the value stocks. (70% * 40) = 28 stocks. He also selected 80% of the growth stocks. (80% * 60) = 48 stocks. So you have his 76 stocks, plus the remaining 12 value stocks (40 - 28) thus 88 / 100 = 88%

Hi Cardshark, thats fine, but why its not tallying with the formula, P(A or B) = P(A) + P(B) - P(AB) = .4 + .76 - .4*.76 = 85.6%

sasankm Card shark is correct. You need to calculate P(A or B) = P(A) + P(B) - P(AB) = .4 + .76 - .4*.7 = 88% Remember P(AB) = P(A│B) * P(B)= P(B│A) * P(A), not P(A)*P(B) To avoid confusion, also good to set up table. Value Growth Total Picked 28 48 76 Not picked 12 12 34 Total 40 60 100

The web does not manage to print out correctly. It should be P (B vertical bar A) or P(B given A has happened) not (B│A) as shown above

CardShark, would you suggest typically breaking out probability problems like you did? It seems more straightforward and more simple that way. Thanks, JM

I’ve always found it easier to do that way. All that P(A), P(B), P(bullshit)…it’s all vanity. If it works for you to break them out easier, go for it.

CardShark Wrote: ------------------------------------------------------- > I’ve always found it easier to do that way. > > All that P(A), P(B), P(bullshit)…it’s all > vanity. > > If it works for you to break them out easier, go > for it. I have to agree with Card Shark. Card Shark’s approach is very straightforward. In fact, I had the same issue with confusing the equations and wound up solving the problems in the same way as Card Shark. Personally, a simple decision tree makes more sense to me than the equations.

This is a great suggestion, thanks.