Thank you for reporting, we will resolve it shortly
Q.
The least number of times a fair coin must be tossed so that the probability of getting at least one head in at least $ 0.8 $ is:
Jharkhand CECEJharkhand CECE 2007
Solution:
Suppose the coin is tossed $ n $ times. Let $ x $ be the number of heads obtained.
Then $ x $ follows a binomial distribution with parameters $ n $ and $ p=\frac{1}{2} $ ,
we have $ p(x\ge 1)\ge 0.8\Rightarrow 1-P(x=0)\ge 0.8 $
$ \Rightarrow $ $ P(x=0)\le 1-0.8=0.2 $
$ \Rightarrow $ $ ^{n}{{C}_{0}}{{\left( \frac{1}{2} \right)}^{n}}\le 0.2=\frac{2}{10}=\frac{1}{5} $
$ \Rightarrow $ $ {{\left( \frac{1}{2} \right)}^{n}}\le \frac{1}{5}\Rightarrow {{2}^{n}}\le 5 $
$ \therefore $ Least value of $ n $ is $ 3 $ .