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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) $$P(A \cap B)$$
$$P(A \cap B)=\varphi$$
$$S \rightarrow n(s)=20$$
$$A \rightarrow P(A)=0,3$$
$$P(A)=\frac{n(A)}{n(S)} $$
$$0,3=\frac{n(A)}{20} \Rightarrow n(A)=0,3 \times 20=6$$
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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) $$P(A \cap B)$$
$$A \cap B=\varphi$$
$$P(A \cap B)=\varphi$$
$$S \rightarrow n(s)=20$$
$$A \rightarrow P(A)=0,3$$
$$P(A)=\frac{n(A)}{n(S)} $$
$$0,3=\frac{n(A)}{20} \Rightarrow n(A)=0,3 \times 20=6$$
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