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If $$P(A)=0.3, P(B)=0.2,$$ and $$P(A \cap B)=0.1$$
$$P(A)=0.3$$ $$P(B)=0.2$$ $$P(A \cap B)=0.1$$
$$P\left(A^{\prime}\right)=1-P(A)=1-0.3=0.7$$
b) $$P(A \cup B)=P(A)+P(B)-P(A \cap B)$$
$$=0.3+0.2-0.1=0.4$$
c) $$P\left(A^{\prime} \cap B\right)$$
$$P(B)=P(A \cap B)+P(A^{\prime} \cap B)$$
$$0.2=0.1+P(A^{\prime} \cap B)$$
$$\Rightarrow P(A^{\prime} \cap B) = 0.1$$
d) $$P\left(A \cap B^{\prime}\right)$$
$$P(A)=P(A \cap B)+P(A \cap B^{\prime})$$
$$0.3=0.1+P(A \cap B^{\prime})$$
$$P(A \cap B^{\prime})=0.2$$
e) $$P\left[(A \cup B)^{\prime}\right]$$
$$=1-P(A \cup B)=0.6$$
f) $$P\left(A^{\prime} \cup B\right)$$
$$=P\left(A^{\prime}\right)+P(B)-P\left(A^{\prime} \cap B\right)$$
$$=0.7+0.2-0.1=0.8$$
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If $$P(A)=0.3, P(B)=0.2,$$ and $$P(A \cap B)=0.1$$
$$P(A)=0.3$$
$$P(B)=0.2$$
$$P(A \cap B)=0.1$$
$$P\left(A^{\prime}\right)=1-P(A)=1-0.3=0.7$$
b) $$P(A \cup B)=P(A)+P(B)-P(A \cap B)$$
$$=0.3+0.2-0.1=0.4$$
c) $$P\left(A^{\prime} \cap B\right)$$
$$P(B)=P(A \cap B)+P(A^{\prime} \cap B)$$
$$0.2=0.1+P(A^{\prime} \cap B)$$
$$\Rightarrow P(A^{\prime} \cap B) = 0.1$$
d) $$P\left(A \cap B^{\prime}\right)$$
$$P(A)=P(A \cap B)+P(A \cap B^{\prime})$$
$$0.3=0.1+P(A \cap B^{\prime})$$
$$P(A \cap B^{\prime})=0.2$$
e) $$P\left[(A \cup B)^{\prime}\right]$$
$$=1-P(A \cup B)=0.6$$
f) $$P\left(A^{\prime} \cup B\right)$$
$$=P\left(A^{\prime}\right)+P(B)-P\left(A^{\prime} \cap B\right)$$
$$=0.7+0.2-0.1=0.8$$
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