Answer :
Given that,
⇒ P(KS) = P(Kamal’s selection)
⇒
⇒ P(KN) = P(Not selecting Kamal)
⇒
⇒
⇒ P(VS) = P(Monika’s selection)
⇒
⇒ P(VN) = P(Not selecting Monika)
⇒
⇒
We need to find:
i. Both of them will be selected
ii. None of them will be selected
iii. At least one of them will be selected
iv. Only one of them will be selected.
⇒ P(Sboth) = P(Both of them are selected)
Since selection of each person is an independent event their probabilities multiply each other
⇒
⇒
⇒
⇒ P(Snone) = P(None of them are selected)
Since selection of each person is an independent event their probabilities multiply each other
⇒
⇒
⇒
⇒ P(Satone) = P(Selecting at least one of them)
⇒ P(Satone) = P(selecting only Kamal) + P(selecting only Monika) + P(Selecting both)
Since selection of each person is an independent event their probabilities multiply each other
⇒
⇒
⇒
⇒
⇒ P(Sone) = P(Only one of them is selected)
⇒ P(Sone) = P(only Kamal is selected) + P(only Monika is selected)
Since selection of each person is an independent event their probabilities multiply each other
⇒
⇒
⇒
∴ The required probabilities are .
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