The following Venn diagram shows a sample space $U$ and events $A$ and $B$. It is known that&n

Question

The following Venn diagram shows a sample space $U$ and events $A$ and $B$. It is known that $n(U)=36$, $n(A)=11$, $n(B)=6$, and $n((A\cup B)\prime)=21$.

On the diagram, shade the region $(A ∪ B)′$.
Find
1. $n(A ∩ B)$;
2. $P(A ∩ B)$.
Explain why events $A$ and $B$ are not mutually exclusive.

[4]

Accepted Answer

(b)(i) $n(A \cap B) = 2$ (b)(ii) $P(A \cap B) = \frac{1}{18}$ (c) $P(A \cap B) \neq 0$

Shade a Venn complement, calculate an intersection and explain non-mutual-exclusivity.

Shade a Venn complement, calculate an intersection and explain non-mutual-exclusivity.

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