smc-4238-60-Arrays

Jon spins each pointer 50 times.

Each time he added the numbers that the pointers landed on.

His results are shown below.

\begin{array} {|c|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex}\textbf{Sum of numbers}\rule[-1ex]{0pt}{0pt} & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 & \textbf{Total}\\
\hline
\rule{0pt}{2.5ex}\textbf{Number of spins}\rule[-1ex]{0pt}{0pt} & 1 & 2 & 3 & 6 & 8 & 9 & 7 & 5 & 4 & 4 & 1 & \textbf{50} \\
\hline
\end{array}

What percentage of the spins resulted in a sum of 9? (2 marks)

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`text(10%)`

Show Worked Solution

`text(Percentage)`	`= text(number of 9’s)/text(number of spins) xx 100`
	`=5/50 xx 100`
	`=10 text(%)`

Bromley rolls two standard dice at the same time and adds up the total.

An incomplete table of the possible outcomes is below.

\begin{array} {|c|c|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex}\textbf{Face} \rule[-1ex]{0pt}{0pt} & \textbf{1} & \textbf{2} & \textbf{3} & \textbf{4} & \textbf{5} & \textbf{6}\\
\hline
\rule{0pt}{2.5ex}\textbf{1}\rule[-1ex]{0pt}{0pt} & 2 & 3 & 4 & 5 & 6 & 7 \\
\hline
\rule{0pt}{2.5ex}\textbf{2}\rule[-1ex]{0pt}{0pt} & 3 & 4 & 5 & & & 8 \\
\hline
\rule{0pt}{2.5ex}\textbf{3}\rule[-1ex]{0pt}{0pt} & 4 & 5 & 6 & & & 9 \\
\hline
\rule{0pt}{2.5ex}\textbf{4}\rule[-1ex]{0pt}{0pt} & 5 & & 7 & 8 & 9 & 10 \\
\hline
\rule{0pt}{2.5ex}\textbf{5}\rule[-1ex]{0pt}{0pt} & 6 & & 8 & & 10 & 11 \\
\hline
\rule{0pt}{2.5ex}\textbf{6}\rule[-1ex]{0pt}{0pt} & 7 & 8 & 9 & 10 & 11 & 12 \\
\hline
\end{array}

Complete the table. (2 marks)

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What is the most likely total that Bromley will roll? (1 mark)

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\begin{array} {|c|c|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex}\textbf{Face} \rule[-1ex]{0pt}{0pt} & \textbf{1} & \textbf{2} & \textbf{3} & \textbf{4} & \textbf{5} & \textbf{6}\\
\hline
\rule{0pt}{2.5ex}\textbf{1}\rule[-1ex]{0pt}{0pt} & 2 & 3 & 4 & 5 & 6 & 7 \\
\hline
\rule{0pt}{2.5ex}\textbf{2}\rule[-1ex]{0pt}{0pt} & 3 & 4 & 5 & \colorbox{lightblue}{6} & \colorbox{lightblue}{7} & 8 \\
\hline
\rule{0pt}{2.5ex}\textbf{3}\rule[-1ex]{0pt}{0pt} & 4 & 5 & 6 & \colorbox{lightblue}{7} & \colorbox{lightblue}{8} & 9 \\
\hline
\rule{0pt}{2.5ex}\textbf{4}\rule[-1ex]{0pt}{0pt} & 5 & \colorbox{lightblue}{6} & 7 & 8 & 9 & 10 \\
\hline
\rule{0pt}{2.5ex}\textbf{5}\rule[-1ex]{0pt}{0pt} & 6 & \colorbox{lightblue}{7} & 8 & \colorbox{lightblue}{9} & 10 & 11 \\
\hline
\rule{0pt}{2.5ex}\textbf{6}\rule[-1ex]{0pt}{0pt} & 7 & 8 & 9 & 10 & 11 & 12 \\
\hline
\end{array}

ii. `7`

Show Worked Solution

\begin{array} {|c|c|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex}\textbf{Face} \rule[-1ex]{0pt}{0pt} & \textbf{1} & \textbf{2} & \textbf{3} & \textbf{4} & \textbf{5} & \textbf{6}\\
\hline
\rule{0pt}{2.5ex}\textbf{1}\rule[-1ex]{0pt}{0pt} & 2 & 3 & 4 & 5 & 6 & 7 \\
\hline
\rule{0pt}{2.5ex}\textbf{2}\rule[-1ex]{0pt}{0pt} & 3 & 4 & 5 & \colorbox{lightblue}{6} & \colorbox{lightblue}{7} & 8 \\
\hline
\rule{0pt}{2.5ex}\textbf{3}\rule[-1ex]{0pt}{0pt} & 4 & 5 & 6 & \colorbox{lightblue}{7} & \colorbox{lightblue}{8} & 9 \\
\hline
\rule{0pt}{2.5ex}\textbf{4}\rule[-1ex]{0pt}{0pt} & 5 & \colorbox{lightblue}{6} & 7 & 8 & 9 & 10 \\
\hline
\rule{0pt}{2.5ex}\textbf{5}\rule[-1ex]{0pt}{0pt} & 6 & \colorbox{lightblue}{7} & 8 & \colorbox{lightblue}{9} & 10 & 11 \\
\hline
\rule{0pt}{2.5ex}\textbf{6}\rule[-1ex]{0pt}{0pt} & 7 & 8 & 9 & 10 & 11 & 12 \\
\hline
\end{array}

ii. `text{The most frequent total = 7 (6 times)}`

`:.\ text{7 is the most likely to be rolled.}`

1st toss	H	H	H	H	T	T	T	T
2nd toss	H	H	T	T	H	H	T	T
3rd toss	H	T	H	T	H	T	H	T
		✓	✓		✓

Probability, SMB-009

Probability, SMB-006

Probability, SMB-001