SOLUTION: 50% people use cell phone for writing notes,40% use paper,20% people use both,if a person is selected at random find the probability that he uses neither for taking notes?

Question 1192319: 50% people use cell phone for writing notes,40% use paper,20% people use both,if a person is selected at random find the probability that he uses neither for taking notes?

Found 2 solutions by Edwin McCravy, greenestamps:
Answer by Edwin McCravy(20081) (Show Source): You can put this solution on YOUR website!

It can be done by formula or Venn diagram. The Venn diagram method is better for understanders. Formulas are better for memorizers. Realize that the probability that a person selected at random fits a certain description is EQUAL TO the percentage of people who fit that certain description Since both "PHONE" and "PAPER" begin with the letter "P", I'll use "PH" for the set of people who use phones (the red circle) and "PA" for the set of people who use paper (the blue circle). The big rectangle contains all the people. Since 20% use both, we put "20%" in the region that in BOTH circles: Since 50% use a phone, the entire red circle must contain 50% and since 20% of the red circle is in the part that is common to both circles, the remaining 50%-20%=30% is already in the left part of the red circle, we must put the other 30% in the left part of the red circle. [Be sure to understand why it couldn't work to put the entire 50% in the left part of the red circle, as many students tend to want to do, because they want to put the whole 50% someplace instead of breaking it down into 20% and 30%.] Since 40% use paper, the entire blue circle must contain 40% and since 20% of the blue circle is in the part that is common to both circles, the remaining 40%-20%=20% is in the right part of the blue circle, so we put the other 20% in the right part of the blue circle. But we have not yet accounted for the percentage of people who use neither phone nor paper. And, that's what we want. So we add what we've accounted for 30%+20%+20%=70% and subtract it from 100%. 100%-70%=30% Then we put 30% outside both circles but inside the rectangle for those who do not use either their phones or paper to write notes. So we see that the answer is 30%. Edwin

Answer by greenestamps(13334) (Show Source): You can put this solution on YOUR website!

Since 20% use both, the 50% the use cell phone consist of 30% who use ONLY cell phone and 20% who use both.

Likewise, the 40% who use paper consist of 20% who use ONLY paper and 20% who use both.

So we have
30% who use cell phone only;
20% who use paper only; and
20% who use both.

That's a total of 70% who use either cell phone or paper; that leaves 30% who use neither.

ANSWER: 30%

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