A) 7
B) 6
C) 5
D) 3
Correct Answer: D
Solution :
Suppose the coin is tossed\[n\]times. Let\[X\]be the number of the heads obtained. Then,\[X\]follows a binomial distribution with parameters\[n\]and\[p=\frac{1}{2}\] Now, \[P(X\ge 1)\ge 0.8\Rightarrow 1-P(X=0)\ge 0.8\] \[\Rightarrow \] \[1{{-}^{n}}{{C}_{0}}{{p}^{0}}{{(1-p)}^{n}}\ge 0.8\] \[\Rightarrow \] \[{{\left( \frac{1}{2} \right)}^{n}}\le 0.2\]or\[{{\left( \frac{1}{2} \right)}^{n}}\le \frac{1}{5}\] \[\Rightarrow \] \[{{2}^{n}}\ge 5\] \[\Rightarrow \] \[n\ge 3\] Hence, the least value of\[n\]is 3.
You need to login to perform this action.
You will be redirected in
3 sec
