Five coins were simultaneously tossed 1000 times and at each toss the number of heads were observed. The number of tosses during which 0, 1, 2, 3, 4 and 5 heads were obtained are shown in the table below. Find the mean number of heads per toss.

No. of heads per toss No. of tosses

0
1
2
3
4
5 38
144
342
287
164
25

Total 1000

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Solution

Given:

First of all prepare the frequency table in such a way that its first column consist of the numnber of heads per tosses and the second column the corresponding number of tosses .

Thereafter multiply the frequency of each row with corresponding values of variable to obtain third column containing.

Then, sum of all entries in the column second and denote by and in the third column to obtain.

We know that mean,
$= \frac{2470}{1000} = 2.47$

Hence, the mean number of heads per toss is 2.47.

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No. of heads per toss (x):	0	1	2	3	4	5
No. of tosses (f):	38	144	342	287	164	25

Three similar coins were tossed simultaneously 500 times and the frequency distribution of heads obtained on each toss is as below.

$\begin{matrix} N u m b e r o f h e a d s & 0 & 1 & 2 & 3 F r e q u e n c y & 60 & 175 & 200 & 65 \end{matrix}$

Find the probability of (i) getting all three heads;

(ii) getting an odd number of heads. [2 MARKS]

Outcome	Two heads	One head	No head
Frequency	24	36	20

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.

Number of Heads	0	1	2	3	4	5	6	7	8
Frequency	2	19	46	62	47	20	5	2	2

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