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Probability, SM-Bank 053

Two unbiased dice,  \(A\)  and  \(B\), with faces numbered  \(1\),  \(2\),  \(3\),  \(4\),  \(5\) and  \(6\) are rolled.

The numbers on the uppermost faces are noted. This table shows all the possible outcomes.

 
\begin{align}
\textbf{Die B } \
\begin{array}{c }
\textbf{Die A } \\
\begin{array}{c|c|c|c|c|c|c}
\ & 1 & 2 & 3 & 4 & 5 & 6  \\
\hline
\ 1 & 1,1 & 1,2 & 1,3 & 1,4 & 1,5 & 1,6  \\
\hline
\ 2 & 2,1 & 2,2 & 2,3 & 2,4 & 2,5 & 2,6  \\
\hline
\ 3 & 3,1 & 3,2 & 3,3 & 3,4 & 3,5 & 3,6  \\
\hline
\ 4 & 4,1 & 4,2 & 4,3 & 4,4 & 4,5 & 4,6  \\
\hline
\ 5 & 5,1 & 5,2 & 5,3 & 5,4 & 5,5 & 5,6  \\
\hline
\ 6 & 6,1 & 6,2 & 6,3 & 6,4 & 6,5 & 6,6  \\
\end{array}
\end{array}
\end{align}

 

A game is played where the difference between the highest number showing and the lowest number showing on the uppermost faces is calculated.

What is the probability that the difference between the numbers showing on the uppermost faces of the two dice is one?   (2 marks)

--- 3 WORK AREA LINES (style=lined) ---

Show Answers Only

\(\dfrac{5}{18}\)

Show Worked Solution

\begin{align}
\textbf{Die B } \
\begin{array}{c }
\textbf{Die A } \\
\begin{array}{c|c|c|c|c|c|c}
\ & 1 & 2 & 3 & 4 & 5 & 6  \\
\hline
\ 1 & 1,1 & \colorbox{lightblue}{1,2} & 1,3 & 1,4 & 1,5 & 1,6  \\
\hline
\ 2 & \colorbox{lightblue}{2,1} & 2,2 & \colorbox{lightblue}{2,3} & 2,4 & 2,5 & 2,6  \\
\hline
\ 3 & 3,1 & \colorbox{lightblue}{3,2} & 3,3 & \colorbox{lightblue}{3,4} & 3,5 & 3,6  \\
\hline
\ 4 & 4,1 & 4,2 & \colorbox{lightblue}{4,3} & 4,4 & \colorbox{lightblue}{4,5} & 4,6  \\
\hline
\ 5 & 5,1 & 5,2 & 5,3 & \colorbox{lightblue}{5,4} & 5,5 & \colorbox{lightblue}{5,6}  \\
\hline
\ 6 & 6,1 & 6,2 & 6,3 & 6,4 & \colorbox{lightblue}{6,5} & 6,6  \\
\end{array}
\end{array}
\end{align}

 

\(\text{# Outcomes with a difference of 1}\)

\(=10\)

\(\therefore\ P \text{(diff of 1)}=\dfrac{10}{36}=\dfrac{5}{18}\)

Filed Under: Probability Tagged With: num-title-ct-core, smc-4225-45-Multi-stage events

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