Percent of non-mutually exclusive x AND y

Question

There are x people in a survey.

y% of people checked box A

z% of people checked box B

It is possible to check BOTH boxes

What percentage of x people checked both boxes?

Am I correct in saying that this question is unanswerable without more information?

Is it possible to check no boxes? Are there more options than just A, B? — nasekatnasushi, Nov 28 '22 at 19:55
It is possible to check no boxes. There are other boxes as well, but they have no bearing on A and B — user3544582, Nov 28 '22 at 19:58
Then you should be able to easily find a concrete example where $ y $ and $ z $ don't uniquely determine the number of people who checked both boxes. — nasekatnasushi, Nov 28 '22 at 20:02

RyRy the Fly Guy · Accepted Answer · 2022-11-28T20:12:20.207

0

The probability of finding box $A$ checked is $y$. The probability of finding box $B$ checked is $z$. If whether or not a person checks $A$ is independent of whether or not a person checks $B$, then the probability of finding both $A$ and $B$ checked is $x=y(z)$. If those two events are in fact dependent, then the answer is not so clear... you would need more information.

edited Nov 28 '22 at 20:12

answered Nov 28 '22 at 20:02

RyRy the Fly Guy

5,950
1
11
27

Thank you. In this example, we're dealing with probabilities, not concrete outcomes correct? – user3544582 Nov 28 '22 at 20:06
Yeah, you can effectively treat the proportions of people who do such and such as probabilities and work solely with those – RyRy the Fly Guy Nov 28 '22 at 20:08
Thank you, much appreciated – user3544582 Nov 28 '22 at 20:10

Percent of non-mutually exclusive x AND y

1 Answers1