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 getting more tails than heads.

Answer 1

Hint: Probability of an event is given as the fraction of the favourable cases for the event and total cases for the problem. Use the given table to get the favourable cases for getting more tails than heads. Hence, use the fundamental expression of probability to get an answer. Mathematically probability can be given as
$P=\dfrac{\text{favourable cases}}{\text{Total cases}}$

Complete step-by-step answer:
Here, we have a table representing the frequency of outcomes for tossing three coins 100 times simultaneously. Table is given in the problem as

Outcome	No head	One head	Two heads	Three heads
Frequency	14	38	36	12

As we know that probability of any event can be given as a fraction of favourable cases and total cases. So, we have
Probability $P=\dfrac{\text{Number of favourable cases}}{\text{Total cases}}$
Now, coming to the question part, as we need to determine the probability of getting more tails than heads by tossing three coins once. Now, we know that the number of tails will be higher on three coins if the number of heads are 0 or 1. In other words we need to determine the probability of getting no head or one head by tossing three coins.
So, we can get the favourable cases for getting more tails than heads are:
Favourable cases = Number of head + Number of one head
=14 + 38 =52.
And the total number of cases = 100. Hence, probability can be given as
$P=\dfrac{52}{100}=\dfrac{13}{25}$
So, probability of getting more tails than heads is $\dfrac{13}{25.}$

Note: One may confuse the question in a way that we have been asked about the probability of getting more tails than heads but we have a table of frequency of heads only. So, one needs to understand that if there is no head on the coin then it will show tail on it. So, don’t be confused with the table and question. So, we can draw a table for tails as

Three tails	2 tails	1 tail	No tail
14	38	36	12

So, it can be another approach for finding the probability for the given condition. Another approach for the question would be that we can get the probability of getting more tails than heads by adding the probabilities of getting one head and zero heads. Answer will remain the same.