Question

Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes:

Outcome	3 heads	2 heads	1 head	No Head
Frequency	23	72	77	28

Find the experimental probability of getting

(i) 2 Heads

(ii) at least 2 Heads

Answer 1

We have,

Outcome	3 heads	2 heads	1 head	No Head
Frequency	23	72	77	28

$$\begin{gathered} \mathrm{As},\mathrm{the}\mathrm{probability}\mathrm{of}\mathrm{an}\mathrm{even}E\mathrm{is}\mathrm{given}\mathrm{by} \\ \mathrm{P}\left(E\right)=\frac{\mathrm{Number}\mathrm{of}\mathrm{favourable}\mathrm{outcomes}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{possible}\mathrm{outcomes}} \\ \mathrm{So}, \\ \left(\mathrm{i}\right)\mathrm{P}\left(2\mathrm{heads}\right)=\frac{72}{200}=\frac{9}{25} \\ \left(\mathrm{ii}\right)\mathrm{P}\left(\mathrm{at}\mathrm{least}2\mathrm{heads}\right)=\mathrm{P}\left(2\mathrm{heads}\right)+\mathrm{P}\left(3\mathrm{heads}\right) \\ =\frac{72}{200}+\frac{23}{200} \\ =\frac{95}{200} \\ =\frac{19}{40} \end{gathered}$$