Question

Two coins are tossed simultaneously $1000$ times with the following frequencies at different outcomes

$\begin{array}{cc}\text{Overhead}& \text{Frequency}\\ 2\text{heads}& 350\\ 1\text{head}& 310\\ \text{No head}& 340\end{array}$

if these two coins are tossed again, find the probability of getting

(i) at least 1 head

(ii) at most one head

Answer 1

Two coins are tossed simultaneously $1000$ times.

Total number of trails $=1000$

Let A: The event of getting at least 1 head.

B: The event of getting at most 1 head.

Number of trials of getting at least 1 head $=$ the sum of the number of trials of getting 1 head and the number of trials of getting 2 heads.

Number of trails of getting at least 1 head $=310+350=660$

Number of trials of getting at most 1 head $=$ the sum of the number of trials of getting 0 head and the number of trials of getting 1 head.

Number of trails of getting at most 1 head $=340+310=650$

(i) $P\left(A\right)=\frac{\text{Number of trails of getting at least 1 head}}{\text{Total number of trails}}=\frac{660}{1000}=0.66$

(ii) $P\left(B\right)=\frac{\text{Number of trials of getting at most 1 head}}{\text{Total number of trails}}=\frac{650}{1000}=0.65$