Question

In order to get a head at least once with probability $\ge 0.9,$ the minimum number of times a unbiased coin needs to be tossed is

• A. $3$
• B. $4$
• C. $5$
• D. $6$

Answer 1

The correct option is B $4$

$P\left(H\right)=\frac{1}{2},P\left(T\right)=\frac{1}{2}$
$P\left(\text{getting atleast one head}\right)=1-P\left(\text{getting no head}\right)$

Let coin tossed $n$ times, then
$P\left(\text{getting atleast one head}\right)=1-{\left(\frac{1}{2}\right)}^n\ge 0.9\Rightarrow 1-\frac{9}{10}\ge \frac{1}{2^n}\Rightarrow \frac{1}{2^n}\le \frac{1}{10}\Rightarrow 10\le 2^n$

The minimum value of $n$ satisfying the above inequality
$n=4$