Question 454001: Chris owns 2 stocks, IBM & GE. The probability that IBM stock will increase in value next year is .5 and the probability that GE stock will increase in value next year is .7. Assume both stocks are independent. What is the probability that at least one of these stocks will increase in value during the next year? (This means that either one can increase or both).
I have an answer of P(at least one)= (.5)(.3)+ (.5)(.7)+ (.7)(.5)=.85
Where does the (.5)(.3) come from??
mkatich@tampabay.rr.com
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Chris owns 2 stocks, IBM & GE. The probability that IBM stock will increase in value next year is .5 and the probability that GE stock will increase in value next year is .7. Assume both stocks are independent. What is the probability that at least one of these stocks will increase in value during the next year? (This means that either one can increase or both).
I have an answer of P(at least one)= (.5)(.3)+ (.5)(.7)+ (.7)(.5)=.85
Where does the (.5)(.3) come from??
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P(IBM increases) = 0.5 ; P(IBM decreases) = 0.5
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P(GE increases) = 0.7 ; P(GE decreases) = 0.3
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So, (0.5)(0.3) is the probability that both decrease,
or it could be the probability that IBM increases and IBM decreases.
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But, here's another way to do the problem:
P(at least one increase)
= 1-P(neither increase)
= 1-(0.5*0.3)
= 1-0.15
= 0.85
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Cheers,
Stan H.
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