Question

A and B are mutually exclusive events, then

• A. $P\left(A\right)\le P\left(\overline{B}\right)$
• B. $P\left(A\right)>P\left(\overline{B}\right)$
• C. $P\left(A\right)<P\left(B\right)$
• D. $P\left(A\right)=P\left(B\right)$

Answer 1

The correct option is A $P\left(A\right)\le P\left(\overline{B}\right)$

If A and B are mutually exclusive this simply means$P(A\cap B)=\varphi \Rightarrow P(A\cup B)\le 1\Rightarrow P\left(A\right)+P\left(B\right)-P(A\cap B)\le 1P(A\cap B)=0,\because (A\cap B)=\varphi \Rightarrow P\left(A\right)\le 1-P\left(B\right)\Rightarrow P\left(A\right)\le P\left(\overline{B}\right)$