Probability and Bayes formula

CFA Level I
#1

“There is a 60% probability that the economy will grow next year. There is a 70% probability of the tech sector outperforming the market if there is economic growth and a 10% probability of outperforming the market if the economy does not grow. Given the new information that the technology sector will not outperform the market, what is the probability that the economy will not expand?”

I have no idea. The book explains the steps to take, but not why we take them. I understand how to solve problems asking for the probability of X given Y if we are given, for example, the probability of Y given X, but I don’t know how to go about solving problems where we are essentially asked to solve for the probability of the complement of X given the complement of Y. Any sugguestions?

#2

Maybe this article I wrote will help: http://financialexamhelp123.com/bayes-formula/.

#3

Yea. It helped. I guess. 66.67%?

#4

There are four possible outcomes:

  1. Economy grows, outperforming tech; probability = 0.42 (= 60% × 70%)
  2. Economy grows, underperforming tech; probability = 0.18 (= 60% × 30%)
  3. Economy doesn’t grow, outperforming tech; probability = 0.04 (= 40% × 10%)
  4. Economy doesn’t grow, underperforming tech; probability = 0.36 (= 40% × 90%)

Given underperforming tech, we have outcome 2 or 4. The probability that the economy doesn’t grow is, thus,

0.36 / (0.18 + 0.36) = 66.67%.

#5

deleted

#6

Um . . . no, no, and no.

See my posts, above.

#7

agreed

#8

Making a tree diagram for these types of questions makes them incredibly easier to understand and answer.

#9

I agree utterly.

#10

Thanks for that.