Question

Mark the correct alternative in the following question:

$$\text{ Let A and B be two events . If }P\left(A\right)=0.2,P\left(B\right)=0.4,P(A\cup B)=0.6,\text{ then }P\left(A|B\right)\text{ is equal to}$$

विकल्प

• 0 . 8 

• 0 . 5 

• 0 . 3 

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Answer 1

$$\text{ We have },$$
$$P\left(A\right)=0.2,P\left(B\right)=0.4\text{ and }P(A\cup B)=0.6$$
$$\text{ As },P(A\cup B)=0.6$$
$$\Rightarrow P\left(A\right)+P\left(B\right)-P(A\cap B)=0.6$$
$$\Rightarrow 0.2+0.4-P(A\cap B)=0.6$$
$$\Rightarrow 0.6-P(A\cap B)=0.6$$
$$\Rightarrow P(A\cap B)=0.6-0.6$$
$$\Rightarrow P(A\cap B)=0$$
$$\text{ Now },$$
$$P\left(A|B\right)=\frac{P(A\cap B)}{P\left(B\right)}=\frac{0}{0.4}=0$$