SOLUTION: A survey of 200 college graduates who have been working for at least 3 years found that 90 owned only mutual funds, 20 owned only stocks, and 70 owned both. What is the probabilit

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Question 1163616: A survey of 200 college graduates who have been working for at least 3 years found that 90 owned only mutual funds, 20 owned only stocks, and 70 owned both.
What is the probability that an individual owns a stock? A mutual fund?
What is the probability that an individual owns neither stocks nor mutual funds?
What is the probability that an individual owns either a stock or a mutual fund?
Found 2 solutions by ikleyn, Edwin McCravy:
Answer by ikleyn(52818)   (Show Source): You can put this solution on YOUR website!
.
A survey of 200 college graduates who have been working for at least 3 years found that
90 owned only mutual funds, 20 owned only stocks, and 70 owned both.
(a) What is the probability that an individual owns a stock?
(b) A mutual fund?
(c) What is the probability that an individual owns neither stocks nor mutual funds?
(d) What is the probability that an individual owns either a stock or a mutual
fund?
~~~~~~~~~~~~~~


Notice that in this problem the mentioned subsets are  DISJOINT.  It is the key to the problem's solution. 


(a)  P =  =  = 0.1.


(b)  P =  =  = 0.8.


(c)  P =  =  =  = 0.1


(d)  P = the complement to the value of (c) = 1 - 0.1 = 0.9.

Solved.


Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!

Ikleyn doesn't like Venn diagrams but prefers inclusion and exclusion
formulas because they are quick and easy.  I prefer Venn diagrams because
they show WHY, not just HOW.




Since 90+70+20=180, then 200-180 = 20 for those outside the circle.

What is the probability that an individual owns a stock? 

P(S) = (70+20)/200 = 90/200 = 9/20 = 0.45

A mutual fund?

P(M) = (90+70)/200 = 160/200 = 4/5 = 0.8

What is the probability that an individual owns neither stocks nor mutual
funds?

P(M' and S') = 20/200 = 1/10 = 0.1


What is the probability that an individual owns either a stock or a mutual
fund?

P(S or M) = (90+70+20)/200 = 180/200 = 9/10 = 0.9

or it's easier just to subtract the last answer from 1, 1 - 0.1 = 0.9

Edwin
 

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