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A coin is tossed three times. What is the probability of getting at least one tail?

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Last updated date: 29th Feb 2024
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IVSAT 2024
Answer
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Hint: In this problem, we have to find the probability of getting at least one tail. We know that a coin has two sides: a head and a tail. If a coin is tossed or flipped there is only one possible either it will be a head or tail. Here in this problem a coin is tossed three times. So we get three results in an outcome.

Complete step-by-step solution:
Here we have to find the probability of getting at least one tail.
A coin is tossed three times here so they may get eight outcomes and three results in an outcome. The outcomes are,
\[\Rightarrow \left\{ HHH,HHT,HTH,THH,TTH,THT,HTT,TTT \right\}\]
Here only one outcome is without a tail, where all those are heads. So the outcomes which are at least one tail are,
\[\Rightarrow \left\{ HHT,HTH,THH,TTH,THT,HTT,TTT \right\}\]
We can see that there are seven outcomes with at least one tail. The total number of outcomes are eight. By using the probability formula, we can solve this problem and find the probability of getting at least one tail when a coin is tossed three times. Let this event be named A. Now we can simplify this problem using formulas.
\[\Rightarrow p\left( A \right)=\dfrac{n\left( A \right)}{n\left( S \right)}\]
Substituting the number of outcomes and total number of outcomes we get,
\[\Rightarrow p\left( A \right)=\dfrac{7}{8}\]
The probability of getting at least one tail when a coin is tossed three times is \[\dfrac{7}{8}\].
Therefore, the solution is \[\dfrac{7}{8}\].

Note:The solved above problem can also be solved through another method by first finding not getting a tail and subtracting it from 1 because to find the probability that there is at least one tail. We need not to find the outcomes , while by doing this method just cubing the solution of not getting a tail is enough hence the coin is tossed three times. Students should read the problem carefully whether it is given a coin is tossed thrice or three coins are tossed.