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Question -

Three coins are tossed simultaneously 100 times with the following frequencies of different outcomes:

Outcome:

No head

One head

Two heads

Three heads

Frequency:

14

38

36

12

If the three coins are simultaneously tossed again, compute the probability of:
(i) 2 heads coming up.
(ii) 3 heads coming up.
(iii) at least one head coming up.
(iv) getting more heads than tails.
(v) getting more tails than heads.



Answer -

The total number of trials is 100.
Remember the empirical or experimental or observed frequency approach to probability.
If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted by  and is given by
 
(i) Let A be the event of getting two heads.
The number of times A happens is 36.
Therefore, we have
(ii) Let B be the event of getting three heads
The number of times B happens is 12.
Therefore, we have
 
(iii) Let C be the event of getting at least one head.
The number of times C happens is  .
Therefore, we have
(iv) Let D be the event of getting more heads than tails.
The number of times D happens is  .
Therefore, we have
 
(v) Let E be the event of getting more tails than heads.
The number of times E happens is  .
Therefore, we have

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