ProbabilityInterpretations And Axioms Of Probability Problems 1

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) $$P(A \cap B)$$

$$A \cap B=\varphi$$

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

$$S \rightarrow n(s)=20$$

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

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

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