Fatima and

Given that,

⇒ P(F_S) = P(Fatima’s selection)

⇒

⇒ P(F_N) = P(Not selecting Fatima)

⇒

⇒

⇒ P(J_S) = P(John’s selection)

⇒

⇒ P(J_N) = P(Not selecting John)

⇒

⇒

We need to find:

i. Both of them will be selected

ii. Only one of them will be selected

iii. None 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_one) = P(Only one of them is selected)

⇒ P(S_one) = P(only Fatima is selected) + P(only John is 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

⇒

⇒

⇒

∴ The required probabilities are .