Question

If three dice are rolled, what is the probability of getting a total of $18$?

Answer 1

Here we have to calculate the probability of getting a total of $18$ when three dice are rolled. So, we have to form Probability of an event can be defined as the ratio of a number of cases favourable to a particular event to the number of all possible cases. Probability can be calculated by the formula:
$P(E) = \dfrac{\text{Number of favourable outcomes to E}}{\text{Number of all possible outcomes of experiment}}$

Complete step by step answer:
We have to calculate the probability of getting a total of $18$ when three dice are rolled.
Probability can be simply defined as the possibility of something happening. It is the extent to which an event is likely to occur, measured by the ratio of the favourable cases to the whole number of cases possible. All the possible outcomes of a random experiment when put together is called a sample space.

The probability of an event can be defined by the following formula:
$P(E) = \dfrac{\text{Number of favourable outcomes to E}}{\text{Number of all possible outcomes of experiment}}$
According to the question three dice are rolled so total number of outcomes $= 6 \times 6 \times 6 = 216$
To obtain a total of $18$ we need all three dice to show $6$
As $6 + 6 + 6 = 18$
So favourable outcomes $= 1$
Therefore, the probability of getting a total of $18$. Use the probability formula which is mentioned above.So,
$\therefore$ $p(E) = \dfrac{1}{{216}}$

Hence, the probability of getting a total of $18$ when three dice are rolled is equal to $\dfrac{1}{{216}}$.

Note: The probability of an impossible event is $0$ and the probability of a sure event is $1$. The probability related to the same event will lie between $0$ and $1$. Hence the probability of an event is always greater or equal than zero but can never be less than zero. For mutually exclusive events, the probability of either of the events happening is the sum of the probability of both the events happening.