Question

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

• A. $7$
• B. $6$
• C. $5$
• D. $3$

Answer 1

The correct option is D $3$

In a single toss, or either get a head or a tail

Probability of getting a head in a single toss = $\frac{1}{2}$

Probability of getting no head in a single toss =1/2

Probability of getting no head in n toss $=(\frac{1}{2}{)}^n$

Probability of getting atleast one head in n tosses

= 1- Probability of getting no heads in a tosses.

$=1-(\frac{1}{2}{)}^n$

and as per question ,

$1-(\frac{1}{2}{)}^n=0.8$

$1-0.8=(\frac{1}{2}{)}^n$

$\Rightarrow 0.2=(\frac{1}{2}{)}^n$

$\Rightarrow 0.2=2^{\frac{1}{2}}$

$\Rightarrow 2^n=\frac{1}{0.2}$

$\Rightarrow 2^n=5$

If $2^1=2<5$

$2^2=4<5$

$2^3=8>5$

$\therefore$ The least number of limits, n=3.