2
$\begingroup$

On a Dart board, with different areas labeled as: A, B, C, D, and each area different sizes. The probabilities of each area are: P(A)=25%, P(B)=50%, P(C)=12.5% and P(D)=12.5%

What is P(~C or B)?

I don't understand the "not C or B" term. If it is not C then it includes B already. My guess would be 87.5%

$\endgroup$
2
  • 3
    $\begingroup$ You did understand the term. The required probability is indeed $0.875$. The mathematical "or" is not quite the ordinary language "or." The event $X$ or $Y$ occurs if $X$ occurs or $Y$ occurs or both occur. $\endgroup$ Sep 22, 2013 at 15:57
  • $\begingroup$ Think of it in terms of sets. Then 'or' becomes $\cup$ and 'and' becomes $\cap$. Hence you have $C^c \cup B = C^c$, since $B \subset C^c$. $\endgroup$
    – copper.hat
    Sep 22, 2013 at 16:23

1 Answer 1

2
$\begingroup$

You understood it correctly. Besides recognizing that mathematically "or" includes both being true, another point was to read it as P((~C) or B) as opposed to P(~(C or B)), which would be 37.5%

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.