Question

Two coins are tossed \[729\] times and the outcomes are: No tail-\[189\], one tail-\[297\], two tails- \[243\]. Find the probability of the occurrence of each of these events.

Answer 1

Hint: In order to find the probability of occurrence of each of these events, we must be using the formula \[\dfrac{\text{favourable outcomes}}{\text{total number of outcomes}}\]. Since we are given the frequency of each outcome and the total number of outcomes, we can easily apply the formula and obtain the required probabilities.

Complete step by step answer:
Now let us briefly talk about probability and its types. Probability can be defined as a chance of a particular event to occur from a set of events. The range of probability is between \[0\] and \[1\]. There are three types of probability. They are: theoretical probability, experimental probability and axiomatic probability. We can define an event as something that takes place.
Now let us start solving the given problem.
So we are given with:
Total number of outcomes when two coins are tossed is \[729\].
The frequency of no tail occurring is \[189\].
The frequency of one tail occurring is \[297\].
The frequency of two tails occurring is \[243\].
Now let us start finding the probability of each of the events by using the formula \[P=\dfrac{\text{favourable outcomes}}{\text{total number of outcomes}}\]
Now, the probability of no tail occurring is-
\[\Rightarrow P=\dfrac{\text{favourable outcomes}}{\text{total number of outcomes}}=\dfrac{189}{729}=\dfrac{7}{27}\]
The probability of one tail occurring is -
\[\Rightarrow P=\dfrac{\text{favourable outcomes}}{\text{total number of outcomes}}=\dfrac{297}{729}=\dfrac{11}{27}\]
The probability of two tails occurring is-
\[\Rightarrow P=\dfrac{\text{favourable outcomes}}{\text{total number of outcomes}}=\dfrac{243}{729}=\dfrac{1}{3}\]
\[\therefore \] The required probabilities are \[\dfrac{7}{27}\], \[\dfrac{11}{27}\] and \[\dfrac{1}{3}\].

Note: We must note that the probabilities are always to be calculated with respect to total number of outcomes. We should always represent a probability in its simplest form possible as it is the most proper way of representing it.