# What is the probability of tossing at least 1 tail if you toss 3 coins at once?

Question
Upper level probability
What is the probability of tossing at least 1 tail if you toss 3 coins at once?

2020-11-10
Lets denote HH after getting heads and TT after getting tails as toss a result. Then after tossing 33 coins we will get following probable cases,
S={HHH,HHT,HTH,THH,HTT,THT,TTH,TTT}
and chances of getting at least one tail if one of following case occurs
ST={HHT,HTH,THH,HTT,THT,TTH,TTT}.
Therefore, probability of getting at least one tail after tossing 3 coins is $$\displaystyle{\left(\frac{{\left|{S}\right|}}{{\left|{S}{t}\right|}}\right)}=\frac{{7}}{{8}}.$$

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