(i) exactly two heads
Possible outcome of tossing three coins are: HTT, HHT, HHH, HTH, TTT, TTH, THT, THH
Numbers of outcomes of exactly two heads are: 3
Probability of getting exactly two heads is = \(\frac{Total\,numbers}{Total\,number\,of\,outcomes}\) = \(\frac{3}{8}\)
Therefore Probability of getting exactly two heads is = \(\frac{3}{8}\)
(ii) at least two heads
Possible outcome of tossing three coins are: HTT, HHT, HHH, HTH, TTT, TTH, THT, THH
Numbers of outcomes of atleast two heads are: 4
Probability of getting atleast two heads is = \(\frac{Total\,numbers}{Total\,number\,of\,outcomes}\) = \(\frac{4}{8}\) = \(\frac{1}{2}\)
Therefore Probability of getting atleast two heads is = \(\frac{1}{2}\)
(iii) at least one head and one tail
Possible outcome of tossing three coins are: HTT, HHT, HHH, HTH, TTT, TTH, THT, THH
Numbers of outcomes of at least one head and one tail are: 6
Probability of getting at least one head and one tail is = \(\frac{Total\,numbers}{Total\,number\,of\,outcomes}\)
= \(\frac{6}{8}\) = \(\frac{3}{4}\)
Therefore Probability of getting at least one head and one tail is = \(\frac{3}{4}\)
(iv) no tails
Possible outcome of tossing three coins are: HTT, HHT, HHH, HTH, TTT, TTH, THT, THH
Numbers of outcomes of no tails are: 1
Probability of getting no tails is = \(\frac{Total\,numbers}{Total\,number\,of\,outcomes}\) = \(\frac{1}{8}\)
Therefore Probability of getting no tails is = \(\frac{1}{8}\)
