A coin is tossed three times. Find `P(E//F)` in each of the following: (i) `E=` Head on the third toss, `F=` Heads on first two tosses (ii) `E=` At least two heads, `F=` At most two heads (iii) `E=` At most two tails, `F=` At least one tail

Explanation

(i) `E = {HHH, HTH,THH, (T,TH)}`

`F = {HHH, HHT}`

`P(E/F)=frac{P(EnnF)}{P(F)}=frac{1/8}{2/8}`


(ii) `E = {HHH, HHT, HTH, THH}`

`F = {HHT, HTH, HT T, THH,THT, T TH, T T T}`

`P(E/F)=frac{P(EnnF)}{P(F)}=frac{3/8}{7/8}=frac{3}{7}`


(iii) `E = {HHH, HHT, HT T, HTH, THH, THT, T TH}`

`F = {HHT, HT T, HTH, THH, THT, T TH, T T T}`

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