Question

Mark the correct alternative in the following question:

$$\text{ If}P\left(A\right)=0.4,P\left(B\right)=0.8\text{ and }P\left(B|A\right)=0.6,\text{ then }P(A\cup B)=$$

Options

• $$0.24$$

• $$0.3$$

• $$0.48$$

• $$0.96$$

Answer 1

$$\text{ We have },$$
$$P\left(A\right)=0.4,P\left(B\right)=0.8\text{ and }P\left(B|A\right)=0.6$$
$$\text{ As, }P\left(B|A\right)=0.6$$
$$\Rightarrow \frac{P(A\cap B)}{P\left(A\right)}=0.6$$
$$\Rightarrow P(A\cap B)=0.6\times P\left(A\right)$$
$$\Rightarrow P(A\cap B)=0.6\times 0.4$$
$$\Rightarrow P(A\cap B)=0.24$$
$$\text{ Now },P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$$
$$=0.4+0.8-0.24$$
$$=1.2-0.24$$
$$=0.96$$