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
If the three coins are simultaneously tossed again , compute the probability of 2 heads coming up .

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Solution

$n = 3$
Probability of getting head $P = \frac{1}{2}$
Probability of not getting head $= q = 1 - \frac{1}{2} = \frac{1}{2}$
It is binomial distribution
$P (x = 2) =^{3} C_{2} P^{2} q^{3 - 2}$
$= 3 C_{1} p^{2} q^{1}$
$= 3 \times {(\frac{1}{2})}^{2} \times = \frac{3}{2^{3}} = \frac{3}{8}$
Number of times $2$ heads comes $= 72$
Total number of times coins were tossed $= 200$
Probability $= \frac{N u m b e r o f t i m e s 2 h e a d c o m e s u p}{T o t a l n u m b e r o f t i m e s t h e c o i n s t w o a r e t o s s e d}$
$= \frac{72}{200} = \frac{9}{25}$

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

If the three coins are simultaneously tossed again, compute the probability of 2 heads coming up.

Outcomes	Frequency
3 heads	23
2 heads	72
1 head	77
No head	28

Q. 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

If the three coins are simultaneously tossed again, compute the
(i) probability of 2 heads coming up.
(ii) probability of 3 tails coming up.

Question 4
Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes:
$\begin{matrix} Out come & 3 heads & 2 heads & 1 head & No head Frequency & 23 & 72 & 77 & 28 \end{matrix}$
If the three coins are simultaneously tossed again, compute the probability of 2 heads coming up.