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[SOLVED] Venn diagram shows a sample space U and events A and B

karush

Well-known member
Jan 31, 2012
2,725
View attachment 1171
(a) the shaded hopefully shows $(A\cup B)'$

(b)
(i) if $(A\cup B)'= 21$ and $n(U)=36$ then $n(A\cup B)=15$
but $n(A)+n(B)=17$ so $n(A\cap B) = 2$

(ii) $P(A\cap B)$ not sure but guessing $2:17$

(c) not sure what "mutually exclusive" means but presume it has to do with the overlap.

never done Venn Diagrams so this is all new ... did look at De Morgan's stuff tho..
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
(a) Correct. Anything that is not in either A or B should be shaded, which is what you did.

(b)

(i) Correct.

(ii) I believe you want to use:

\(\displaystyle P(A\cap B)=\frac{n(A\cap B)}{n(U)}\)

(c) Two sets are mutually exclusive if:

\(\displaystyle A\cap B=\emptyset\)
 

karush

Well-known member
Jan 31, 2012
2,725
(a)

(ii) I believe you want to use:

\(\displaystyle P(A\cap B)=\frac{n(A\cap B)}{n(U)}\)
so

$\displaystyle P(A\cap B)=\frac{n(A\cap B)}{n(U)}=

\frac{2}{36}=\frac{1}{16}$
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
so

$\displaystyle P(A\cap B)=\frac{n(A\cap B)}{n(U)}=

\frac{2}{36}=\frac{1}{16}$
Not quite...

\(\displaystyle \frac{2}{36}=\frac{2}{2\cdot18}=\frac{1}{18}\)

:D