JEE-Advanced 2015 (3/40)

Probability Level 3

What is the minimum number of times a fair coin needs to be tossed, so that the probability of getting at least two heads is at least 0.96?

1 solution

Shaun Leong
Aug 13, 2016

Let $n$ be the number of times needed.

There are $2^n$ total ways, with $n$ ways to get $1$ head and $1$ way to get $0$ heads.

Thus we have $\frac{2^n-n-1}{2^n}>0.96$ $1-\frac{n+1}{2^n}>0.96$ $\frac{n+1}{2^n}<0.04$

Since $n=7$ does not satisfy the condition but $n=8$ does, we have $\boxed{n=8}$

Isnt it $\geq$

Md Zuhair - 4 years, 2 months ago