(i) A coin has two sides a head(H) and a tail(T), and there are two such coins.

∴ There are X^m possible outcomes.

That is 2² = 4 and they are HH, HT, TH, TT

∴  All possible outcomes are HH, HT, TH, TT.

Total number of outcomes = 4 

Chances of getting 2 tails = 1, that is TT

Probability (P) = \(\frac{Number\,of\,favorable\,outcomes}{Total\,number\,of\,outcomes}\)

∴ Probability of getting a tail P(both T)

= \(\frac{Number\,of\,times\,two\,tails\,occured}{Total\,number\,of\,outcomes\,when\,a\,coin\,is\,tossed}\) = \(\frac{1}{4}\)

(ii) A coin has two sides a head(H) and a tail(T), and there are two such coins.

∴ There are X^m possible outcomes.

That is 2² = 4 and they are HH, HT, TH, TT

∴ All possible outcomes are HH, HT, TH, TT.

Total number of outcomes = 4 

Chances of getting at least one tail = 3, that is HT, TH, TT.

Probability (P) = \(\frac{Number\,of\,favorable\,outcomes}{Total\,number\,of\,outcomes}\)

∴ Probability of getting a tail P(atleast 1 T)

= \(\frac{Number\,of\,times\,atleast\,1\,tail\,occured}{Total\,number\,of\,outcomes\,when\,a\,coin\,is\,tossed}\) = \(\frac{3}{4}\)

(iii) A coin has two sides a head(H) and a tail(T), and there are two such coins.

∴ There are X^m possible outcomes.

That is 2² = 4 and they are HH, HT, TH, TT

∴ All possible outcomes are HH, HT, TH, TT. 

Total number of outcomes = 4 

Chances of getting at most 1 tail = 3, that is HT, TH, TT.

Probability (P) = \(\frac{Number\,of\,favorable\,outcomes}{Total\,number\,of\,outcomes}\)

∴ Probability of getting a tail P(atmost 1 T)

= \(\frac{Number\,of\,times\,atleast\,1\,tail\,occured}{Total\,number\,of\,outcomes\,when\,a\,coin\,is\,tossed}\) = \(\frac{3}{4}\)