Question

Two coins are tossed $1000$ times and the outcomes are recorded as given below:
$\begin{array}{cccc}\text{Number of heads}& 0& 1& 2\\ \text{Frequency}& 240& 450& 310\end{array}$
In a simple throw of two coins, what is the probability of getting

(i) at most one head?

(ii) at least one head?

Answer 1

Given, total number of tosses $=1000$, In which

Number of times $2$ heads appear $=310$

Number of times $1$ head appears $=450$

Number of times $0$ head appears $=240$

Since, probability of an even $A=\frac{\text{number of favourable outcomes to A}}{\text{total number of possible outcomes}}$

(i) Let $E_1$ be the event of getting at most $1$ head.

Then, number of favourable outcomes for $E_1$​ (either $1$ head or $0$ head) $=(450+240)=690$

P(getting at most $1$ head) $=P\left(E_1\right)=\frac{(450+240)}{1000}$
$=\frac{690}{1000}$
$=\frac{69}{100}$
$\therefore P\left(E_1\right)=0.69$
(ii) Let $E_2$ be the event of getting at least $1$ head.

Then, number of favourable outcomes for $E_2$ ​​(either $1$ head or $2$ heads appear) $=450+310=760$

P( getting at least $1$ head) $P\left(E_2\right)=\frac{760}{1000}$
$=\frac{19}{25}$
$\therefore P\left(E_2\right)=0.76$