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• Notes

Each of the possible five outcomes of a random ex-
periment is equally likely. The sample space is $\{a, b, c, d, e\}$
Let $A$ denote the event $\{a, b\},$ and let $B$ denote the event
$\{c, d, e\} .$ Determine the following:

(a) $P(A) \quad$ (b) $P(B)$
(c) $P\left(A^{\prime}\right) \quad$ (d) $P(A \cup B)$
(e) $P(A \cap B)$

$S=\{a, b, c, d, e\}$

$A=\{a, b\}$

$B=\left\{c, d, e\right\}$

a) $P(A) \rightarrow P(A)=\frac{n(A)}{n(S)}=\frac{2}{5}$

b) $P(B) \rightarrow P(B)=\frac{n(B)}{n(S)}=\frac{3}{5}$

c) $P\left(A^{\prime}\right) \rightarrow P\left(A^{\prime}\right)=1-P(A)$

$=1-\frac{2}{5}=\frac{3}{5}$

d) $P(A \cup B)$

$A \cap B=\varphi$

$P(A \cup B)=P(A)+P(B)$

$=\frac{2}{5}+\frac{3}{5}=1$

e) $P(A \cap B)$

$A \cap B=\varphi$

$P(A \cap B)=\varphi$

$S \rightarrow n(s)=20$

$A \rightarrow P(A)=0,3$

$P(A)=\frac{n(A)}{n(S)}$

$0,3=\frac{n(A)}{20} \Rightarrow n(A)=0,3 \times 20=6$