Question

Mark the correct alternative in the following question:

$$\begin{gathered} \mathrm{If}\mathrm{P}\left(A\right)=0.4,\mathrm{P}\left(B\right)=0.8\mathrm{and}\mathrm{P}\left(B|A\right)=0.6,\mathrm{then}\mathrm{P}\left(A\cup B\right)= \\ \left(\mathrm{a}\right)0.24\left(\mathrm{b}\right)0.3\left(\mathrm{c}\right)0.48\left(\mathrm{d}\right)0.96 \end{gathered}$$

Answer 1

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

Hence, the correct alternative is option (d).