Answer :

Given that,

⇒ P(K_{S}) = P(Kamal’s selection)

⇒

⇒ P(K_{N}) = P(Not selecting Kamal)

⇒

⇒

⇒ P(V_{S}) = P(Monika’s selection)

⇒

⇒ P(V_{N}) = 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(S_{both}) = P(Both of them are selected)

Since selection of each person is an independent event their probabilities multiply each other

⇒

⇒

⇒

⇒ P(S_{none}) = P(None of them are selected)

Since selection of each person is an independent event their probabilities multiply each other

⇒

⇒

⇒

⇒ P(S_{atone}) = P(Selecting at least one of them)

⇒ P(S_{atone}) = 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(S_{one}) = P(Only one of them is selected)

⇒ P(S_{one}) = 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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