Question

There are $1$ to $30$ numbers on the circular dice. If we rotate two times, both the time $11$ appears on the dice is _____
a. $\dfrac{1}{{60}}$
b. $\dfrac{1}{{30}}$
c. $\dfrac{1}{{900}}$
d. $\dfrac{{11}}{{30}}$

Answer 1

As we know that the above question is related to probability. Probability is the prediction of a particular outcome of a random event. We know that in case of a random experiment, an event is a set of possible outcomes at a specified condition. We can say that the probability is $P(E) =$ $\dfrac{{n(A)}}{{n(S)}}$, where $n(A)$ is the number of outcomes favourable to A and $n(S)$ is the number of all possible outcomes of the experiment.

Complete step by step answer:
Here in the above question we have a circular dice on which numbers are $1$ to $30$. It is rotated two times and we have to find the probability of $11$ on the dice, twice.
Since both are independent events, So when the first dice is rotated, the probability of getting $11$ is $\dfrac{{n(A)}}{{n(S)}} = \dfrac{1}{{30}}$. It can appear only once.
When again the dice is rotated, the probability of getting $11$ is only once i.e. $\dfrac{1}{{30}}$.
So the probability of $11$ both times is $\dfrac{1}{{30}} \times \dfrac{1}{{30}} = \dfrac{1}{{900}}$.

Hence the correct answer is $c)\dfrac{1}{{900}}$.

Note: Before solving this we should know that both the events i.e. having $11$ twice is an independent event. It means that we can say two events are independent if knowing that one event occurred does not change the probability of the other event. We should have the proper knowledge of probability and their formulas before solving this kind of question.