Question

If two dice are thrown together. Then what is the probability that at least one dice shows the digit 6?
A. \[\dfrac{{11}}{{36}}\]
B. \[\dfrac{{36}}{{11}}\]
C. \[\dfrac{5}{{11}}\]
D. \[\dfrac{1}{6}\]

Answer 1

Hint: First find the possible outcomes of the both dice. Then calculate the outcomes where at least one digit 6 is present. In the end, use the formula of probability to get the required answer.

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

Complete step by step solution:
Given: Two dice are thrown together.
The possible outcomes are:
\[\left\{ \begin{array}{l}\left( {1,1} \right),\left( {1,2} \right),\left( {1,3} \right),\left( {1,4} \right),\left( {1,5} \right),\left( {1,6} \right),\\\left( {2,1} \right),\left( {2,2} \right),\left( {2,3} \right),\left( {2,4} \right),\left( {2,5} \right),\left( {2,6} \right),\\\left( {3,1} \right),\left( {3,2} \right),\left( {3,3} \right),\left( {3,4} \right),\left( {3,5} \right),\left( {3,6} \right),\\\left( {4,1} \right),\left( {4,2} \right),\left( {4,3} \right),\left( {4,4} \right),\left( {4,5} \right),\left( {4,6} \right),\\\left( {5,1} \right),\left( {5,2} \right),\left( {5,3} \right),\left( {5,4} \right),\left( {5,5} \right),\left( {5,6} \right),\\\left( {6,1} \right),\left( {6,2} \right),\left( {6,3} \right),\left( {6,4} \right),\left( {6,5} \right),\left( {6,6} \right)\end{array} \right\}\]
So, total number of outcomes \[ = 36\]
Let \[E\] be the event where at least one dice shows the digit 6.
Then, the probability of the event \[E\] is the probability that one dice shows digit 6 and both dice show digit 6.
The possible outcomes of event \[E\] are:
\[\left\{ {\left( {1,6} \right),\left( {2,6} \right),\left( {3,6} \right),\left( {4,6} \right),\left( {5,6} \right),\left( {6,1} \right),\left( {6,2} \right),\left( {6,3} \right),\left( {6,4} \right),\left( {6,5} \right),\left( {6,6} \right)} \right\}\]
So, the number of favourable outcomes \[ = 11\]
Now apply the formula of the probability of an event.
The probability that at least one dice shows the digit 6 is:
\[P\left( E \right) = \dfrac{{11}}{{36}}\]
Hence the correct option is A.

Note: Students often get confused about the probability of at least terms. In this condition, we also have to consider all possible situations where the number presents more than or equal to the least number.