Question

Câu 8: Cho các biến cố A, B thỏa mãn \( P(A \cap B) = \frac{1}{6} \); \( P(A \cap \overline{B}) = \frac{1}{4} \); \( P(B) = \frac{2}{3} \)

a) \( P(\overline{B}) = \frac{1}{3} \).

b) \( P(A \setminus B) = \frac{1}{9} \).

c) \( P(A \setminus \overline{B}) = \frac{3}{4} \).

d) \( P(A) = \frac{1}{5} \).

Answer 1

\(a.P\left(\overline{B}\right)=1-P\left(B\right)=1-\dfrac{2}{3}=\dfrac{1}{3}\RightarrowĐúng\)

\(b.P\left(A|B\right)=P\left(A\cap\overline{B}\right)=\dfrac{1}{4}\Rightarrow Sai\)

\(c.P\left(A|\overline{B}\right)=P\left(A\cap B\right)=\dfrac{1}{6}\Rightarrow Sai\)

\(d.P\left(A\right)=P\left(A|B\right)+P\left(A|\overline{B}\right)=\dfrac{1}{6}+\dfrac{1}{4}=\dfrac{5}{12}\Rightarrow Sai\)