"In a recent survey it was found that 50% of investors placed their money in Apple shares while 60% invested in Google. Of the people surveyed, 15% invested in neither of these. Find the proportion of investors that had both Apple and Google shares." I have tried calculating as two independent events: Pr(AcapB)=Pr(A)*Pr(B)=0.5*0.6=0.3, which is incorrect. According to the answers, the correct answer should be 0.25, but I'm not able to find this at all. Any help is greatly appreciated!

opinaj 2022-09-29 Answered
"In a recent survey it was found that 50% of investors placed their money in Apple shares while 60% invested in Google. Of the people surveyed, 15% invested in neither of these.
Find the proportion of investors that had both Apple and Google shares."
I have tried calculating as two independent events:
P r ( A B ) = P r ( A ) P r ( B ) = 0.5 0.6 = 0.3 ,
which is incorrect.
According to the answers, the correct answer should be 0.25, but I'm not able to find this at all. Any help is greatly appreciated!
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Answers (1)

Sanaa Hudson
Answered 2022-09-30 Author has 7 answers
P ( A ) = 0.5 , P ( G ) = 0.6
1 P ( A G ) = 0.15
P ( A G ) = 0.85
P ( A ) + P ( G ) P ( A G ) = 0.85
0.5 + 0.6 P ( A G ) = 0.85
P ( A G ) = 1.1 0.85 = 0.25
The reason your method doesn't work is because the event of buying apple stocks and google stocks are not independent.
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