Quantitative Methods Q187

0. The probability of boom is 60% and the probability of recession is 40% for the economy of Lorekia. If Lorekia’s economy is in a boom, the probability of Stock LMN outperforming is 85%, and the probability of the stock underperforming is 15%. On the other hand, during a recession, there is a 20% probability that Stock LMN will outperform and an 80% probability that it will underperform. The probability of the economy being in a recession, given that LMN is outperforming is closest to:

Answer
Comment
Array

Option : A
Explanation : First, list the various probabilities given and determine the probability to be calculated:
P (Boom) = 0.60
P (Recession) = 0.40
P (Outperform | Boom) = 0.85
P (Underperform| Boom) = 0.15
P (Outperform | Recession) = 0.20
P (Underperform | Recession) = 0.80
P (Recession | Outperform)
= [ P (Outperform | Recession) * P (Recession) ] / { [ P (Outperform | Recession) * P (Recession) ] + [ P (Outperform | Boom) * P (Boom) ] } P (Recession | Outperform) = ( 0.20 * 0.40 ) / [ ( 0.20 * 0.40) + ( 0.85 * 0.60 ) ]

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