Question

Mark the correct alternative in the following question:

If two events are independent, then

(a) they must be mutually exclusive
(b) the sum of their probabilities must be equal to 1
(c) (a) and (b) both are correct
(d) none of the above is correct

Answer 1

$$\begin{gathered} \mathrm{Let}A\mathrm{and}B\mathrm{are}\mathrm{two}\mathrm{independent}\mathrm{events}.\mathrm{Then}, \\ \mathrm{P}\left(A\cap B\right)=\mathrm{P}\left(A\right)\times \mathrm{P}\left(B\right) \\ \mathrm{As},\mathrm{P}\left(A\cap B\right)\ne 0\mathrm{or}\mathrm{P}\left(A\right)+\mathrm{P}\left(B\right)\ne 1 \\ \mathrm{So},\mathrm{both}\mathrm{are}\mathrm{neither}\mathrm{mutually}\mathrm{exclisive}\mathrm{nor}\mathrm{their}\mathrm{sum}\mathrm{of}\mathrm{probabilities}\mathrm{is}1. \end{gathered}$$

Hence, the correct alternative is option (d).