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 the value of n equals

• A. 10
• B. 15
• C. 12
• D. 5

Answer 1

The correct option is D 5

Probability of getting atleast one head in n trials
$=1-\frac{1}{2^n}$.
Probability of getting atleast two heads
$=1-\frac{1}{2^n}-\frac{{}^n{C}_1}{2^n}$
Subtracting ii from i we get
$1-\frac{1}{2^n}-(1-\frac{1}{2^n}-\frac{{}^n{C}_1}{2^n})$
$=\frac{{}^n{C}_1}{2^n}$
$=\frac{n}{2^n}=\frac{5}{32}$
Hence n=5.