Question

A student argues that there are 11 possible outcomes 2,3,4,5,6,7,8,9,10,11,12. Therefore, each of them has a probability $\dfrac{1}{{11}}$ . Do you agree with this argument? Justify your answer.

Answer 1

Hint: In this question we have to argue whether the probability of occurrence of any one event is $\dfrac{1}{{11}}$ or not. This question is simply based on the definition of probability. Here we will first find the favourable events and then use a formula for finding the probability.

Complete step-by-step answer:

In the question, we have 11 outcomes. So, we can write:
Sample space of total outcomes =$\left\{ {2,3,4,5,6,7,8,9,10,11,12} \right\}$ .
We have to argue whether each of the outcomes has a probability of $\dfrac{1}{{11}}$ or not.
From the above sample space of total outcomes, we can say that each of the outcomes is distinct or unique.
Now, we know that the formula for finding probability is given as:
Probability = $\dfrac{{{\text{Total number of favourable events}}}}{{{\text{Total number of possible events}}}}$.
For selecting any one of the outcome, we will use combination which gives:
Number of ways of selection of any one event =${}^{11}{{\text{C}}_1}$ = Total number of possible events.
Now, each of the number in sample space can occurred in 1 way
$\therefore $ Number of favourable events =1
Now, probability of occurrence of each of the outcome is given as:
Probability = $\dfrac{{{\text{Total number of favourable events}}}}{{{\text{Total number of possible events}}}} = \dfrac{1}{{11}}$.
Therefore, it is verified that the probability of each outcome of the sample space is $\dfrac{1}{{11}}$.

Note: Before solving this type of question you should remember the formula for finding the probability. Here the sample space for total outcome is given. You should know that each of the distinct numbers of the sample space can occur in 1 way. So, the number of favourable events is 1 and then calculate the total possible events. Finally use the formula for finding the probability.