Angelo studied the report by an analyst that predicted the probabiliti

Question

https://gmatclub.com/forum/download/file.php?id=54937 Angelo studied the report by an analyst that predicted the probabilities of the returns four stocks may generate in the next one year. Based on the probabilities of the returns, Angelo invested $100 each in four stocks for a year. He plans to sell a stock at the end of the year if the stock is valued at not less than $140. What is the probability that Angelo sells at least 1 of the stocks? A. 0.011 B. 0.021 C. 0.979 D. 0.989 E. 1 1.png

Archit3110 · Answer

see table column 2 are referring to stocks with % >=40 ; so we get P of not getting >=40 would be 
.3*.7*.5*.2 ; .021
so probability that Angelo sells at least 1 of the stocks ; 1-.021 ; .979
OPTION C

NitishJain · Answer

IMO  C

P(Angelo sells at least 1 of the stocks) = 1 - P(Angelo do not sell any stock)

Angelo do not sell any stock when all stocks market value is less than $140 or less than 40% return
P(Angelo do not sell any stock) = P(Angelo do not sell first stock) * P(Angelo do not sell second stock)* P(Angelo do not sell third stock) * P(Angelo do not sell fourth stock)

= P(return less than 40% for stock 1) * P(return less than 40% for stock 2) * P(return less than 40% for stock 3) * P(return less than 40% for stock 4) 
 = 3/10 * 7/10 * 5/10 *2/10 = 0.021

P(Angelo sells at least 1 of the stocks) = 1- 0.021 = 0.979

SiffyB · Answer

Bunuel , this is a question by egmat.

MangoMediterraneo · Answer

Hi, is there a way to solve the exercise using directly the probability that the stock performs greater than 40% (for example 0.7 for stock 1, 0.3 for stock 2...)?
I know that we can solve the exercise faster using the "at least trick", but I'd like to understand this alternative solution, to have an overview of all the methods.
Thanks

siddhantvarma · Answer

You'll have to consider various cases. P(at least 1) means P(1 stock) + P(2 stocks) + P(3 stocks) + P(4 stocks)
Now, for each case, you'll have multiple scenarios:
P(1 stock) = P(1>=40%) + P(2>=40%) + P(3>=40%) + P(4>=40%)
P(2 stocks) = P(1>=40%)*P(2>=40%) + P(1>=40%)*P(3>=40%) + ....
...

Similarly, you'll need to write down cases of 3 stocks and for all 4. You can see where it goes using this method, but it's not feasible to calculate this, especially under time constraints. So even if you did think of this in the exam, you'll have to do the reverse since there you're only calculating probability for 1 case.

Angelo studied the report by an analyst that predicted the probabiliti

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