A) 7
B) 6
C) 5
D) None of these
Correct Answer: D
Solution :
Suppose the coin 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, \[P(X\ge 1)\ge 0.8\Rightarrow 1-P(X=0)\ge 0.8\] Þ \[1{{-}^{n}}{{C}_{0}}{{P}^{0}}{{(1-P)}^{n}}\ge 0.8\] \[\Rightarrow {{\left( \frac{1}{2} \right)}^{n}}\le 0.2\Rightarrow {{\left( \frac{1}{2} \right)}^{n}}=\frac{1}{5}\Rightarrow {{2}^{n}}\ge 5\] This shows that the least value of n is 3.
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