Two different coins are tossed simultaneously. Find the probability of getting :

(i) two tails

(ii) one tail

(iii) no tail

(iv) atmost one tail.

When two different coins are tossed simultaneously, then sample space = {HH, HT, TH, TT}. It consists of 4 equally likely outcomes.

Total number of possible outcomes = 4.

(i) Let A be the event 'two tails', then A = {TT} and the number of outcomes favourable to the event A = 1.

∴ P(two tails) = $\dfrac{1}{4}$.

Hence, the probability of getting two tails = $\dfrac{1}{4}$.

(ii) Let B be the event 'one tail', then A = {HT, TH} and the number of outcomes favourable to the event B = 2.

∴ P(one tail) = $\dfrac{2}{4} = \dfrac{1}{2}$.

Hence, the probability of getting one tail = $\dfrac{1}{2}$.

(iii) Let C be the event 'no tail', then C = {HH} and the number of outcomes favourable to the event C = 1.

∴ P(no tail) = $\dfrac{1}{4}$.

Hence, the probability of getting no tail = $\dfrac{1}{4}$.

(iv) Let D be the event 'atmost one tail', then D = {HH, HT, TH} and the number of outcomes favourable to the event D = 3.

∴ P(atmost one tail) = $\dfrac{3}{4}$.

Hence, the probability of getting atmost one tail = $\dfrac{3}{4}$.