Question

A coin is tossed $n$ times. The probability of getting at least one head is greater than that of getting at least two tails by $\frac{5}{32}$. Then, $n$ is

• A. $15$
• B. $5$
• C. $10$
• D. none of these

Answer 1

The correct option is B $5$

$P(H\ge 1)=1-{\left(\frac{1}{2}\right)}^n$
$P(T\ge 2)=1-{\left(\frac{1}{2}\right)}^n-\frac{n}{2^n}$
$P(H\ge 1)-P(T\ge 2)=\frac{n}{2^n}$
$\frac{5}{32}=\frac{n}{2^n}$
Hence, $n=5$