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

#### karush

##### Well-known member
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

Staff member
(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
(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

$\displaystyle P(A\cap B)=\frac{n(A\cap B)}{n(U)}= \frac{2}{36}=\frac{1}{16}$
$$\displaystyle \frac{2}{36}=\frac{2}{2\cdot18}=\frac{1}{18}$$