Question

The minimum number of times a fair coin must be tossed so that the probability of getting at least one head is at least 0.8, is

• A. 7
• B. 6
• C. 5
• D. 3

Answer 1

The correct option is D 3

Let $n$ number of tosses are required.
Now probability of getting head in one trial is, $p=\frac{1}{2}=$ success
Thus probability of getting at least one head in $n$ tosses is $=1-P(X=0)=1{-}^n{C}_0(1-p{)}^n=1-\frac{1}{2^n}\ge .8$ (given)
$\Rightarrow \frac{1}{2^n}\le .2$
Now when $n=1,\frac{1}{2^n}=.5$, $n=2,\frac{1}{2^n}=.25$, $n=3,\frac{1}{2^n}=.125$
Hence minimum number of tosses required is 3.