Question

Three dice are thrown simultaneously. Then find the probability of containing a total of \[17\] or \[18\].
A. \[\dfrac{1}{9}\]
B. \[\dfrac{1}{{72}}\]
C. \[\dfrac{1}{{54}}\]
D. None of these

Answer 1

Hint: In the given question, three dice are thrown simultaneously. The possible number of sample spaces are \[{6^3}\]. Then find the possible number of ways, where the total is \[17\] and \[18\]. By using the probability formula, we will find the probability of containing a total of \[17\] or \[18\].

Formula Used:
Probability Formula:
The probability of an event \[E\] is: \[P\left( E \right) = \dfrac{{The number of favourable outcomes}}{{Total number of outcomes}}\]

Complete step by step solution:
The three dice are thrown simultaneously.
When we throw three dice, then the total number of outcomes is \[{6^3} = 216\]

The sample space for getting a sum of \[17\]: \[\left\{ {\left( {5,6,6} \right),\left( {6,5,6} \right),\left( {6,6,5} \right)} \right\}\]
The sample space for getting a sum of \[18\]: \[\left\{ {\left( {6,6,6} \right)} \right\}\]
So, the number of favourable outcomes is \[ = 4\]

Now apply the probability formula to calculate the probability of containing a total of \[17\] or \[18\].
The probability of containing a total of \[17\] or \[18\]\[ = \dfrac{4}{{216}}\]
\[ \Rightarrow \] The probability of containing a total of \[17\] or \[18\]\[ = \dfrac{1}{{54}}\]
Hence the correct option is C.

Note: Probability means how likely something is to happen. The range of the probability lies between 0 and 1.
The sum of the probabilities of an event and the probability of its complement is 1.