A) \[3\]
B) \[6\]
C) \[5\]
D) none of these
Correct Answer: A
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\[3\].
You need to login to perform this action.
You will be redirected in
3 sec
