Two coins are tossed once, where

(i) E : tail appears on one coin, F : one coin shows head

(ii) E : no tail appears, F : no head appears

Determine P(E|F)

The sample space of the given experiment will be:

S = {HH, HT, TH, TT}

(i) Here, E: tail appears on one coin

And F: one coin shows head

⇒ E = {HT, TH} and F = {HT, TH}

⇒ E ∩ F = {HT, TH}

So,

Now, we know that

By definition of conditional probability,

⇒ P(E|F) = 1

(ii) Here, E: no tail appears

And F: no head appears

⇒ E = {HH} and F = {TT}

⇒ E ∩ F = ϕ

So,

Now, we know that

By definition of conditional probability,

⇒ P(E|F) = 0