Aussie Maths & Science Teachers: Save your time with SmarterEd
A roulette wheel has the numbers 0, 1, 2, …, 36 where each of the 37 numbers is equally likely to be spun.
If the wheel is spun 18 500 times, calculate the expected frequency of spinning the number 8. (2 marks)
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Jeremy rolled a biased 6-sided die a number of times. He recorded the results in a table.
\begin{array} {|l|c|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} \text{Number} \rule[-1ex]{0pt}{0pt} & \ \ 1 \ \ & \ \ 2 \ \ & \ \ 3 \ \ & \ \ 4 \ \ & \ \ 5 \ \ & \ \ 6 \ \ \\
\hline
\rule{0pt}{2.5ex} \text{Frequency} \rule[-1ex]{0pt}{0pt} & \ \ 23 \ \ & \ \ 19 \ \ & \ \ 48 \ \ & \ \ 20 \ \ & \ \ 21 \ \ & \ \ 19 \ \ \\
\hline
\end{array}
What is the relative frequency of rolling a 3? (1 mark)
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The table shows the relative frequency of selecting each of the different coloured jelly beans from packets containing green, yellow, black, red and white jelly beans.
\begin{array} {|c|c|}
\hline
\rule{0pt}{2.5ex} \textit{Colour} \rule[-1ex]{0pt}{0pt} & \textit{Relative frequency} \\
\hline
\rule{0pt}{2.5ex} \text{Green} \rule[-1ex]{0pt}{0pt} & 0.32 \\
\hline
\rule{0pt}{2.5ex} \text{Yellow} \rule[-1ex]{0pt}{0pt} & 0.13 \\
\hline
\rule{0pt}{2.5ex} \text{Black} \rule[-1ex]{0pt}{0pt} & 0.14 \\
\hline
\rule{0pt}{2.5ex} \text{Red} \rule[-1ex]{0pt}{0pt} & \\
\hline
\rule{0pt}{2.5ex} \text{White} \rule[-1ex]{0pt}{0pt} & 0.24 \\
\hline
\end{array}
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Marcella is planning to roll a standard six-sided die 60 times.
How many times would she expect to roll the number 4?
A die has faces numbered 1 to 6. The die is biased so that the number 6 will appear more often than each of the other numbers. The numbers 1 to 5 are equally likely to occur.
The die was rolled 1200 times and it was noted that the 6 appeared 450 times.
Which statement is correct?
A die was rolled 72 times. The results for this experiment are shown in the table.
\begin{array} {|c|c|}
\hline
\rule{0pt}{2.5ex} \textit{Number obtained} \rule[-1ex]{0pt}{0pt} & \textit{Frequency} \\
\hline
\rule{0pt}{2.5ex} \ 1 \rule[-1ex]{0pt}{0pt} & 16 \\
\hline
\rule{0pt}{2.5ex} \ 2 \rule[-1ex]{0pt}{0pt} & 11 \\
\hline
\rule{0pt}{2.5ex} \ 3 \rule[-1ex]{0pt}{0pt} & \textbf{A} \\
\hline
\rule{0pt}{2.5ex} \ 4 \rule[-1ex]{0pt}{0pt} & 8 \\
\hline
\rule{0pt}{2.5ex} \ 5 \rule[-1ex]{0pt}{0pt} & 12 \\
\hline
\rule{0pt}{2.5ex} \ 6 \rule[-1ex]{0pt}{0pt} & 15 \\
\hline
\end{array}
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In an experiment, two unbiased dice, with faces numbered 1, 2, 3, 4, 5, 6 are rolled 18 times.
The difference between the numbers on their uppermost faces is recorded each time. Juan performs this experiment twice and his results are shown in the tables.
Juan states that Experiment 2 has given results that are closer to what he expected than the results given by Experiment 1.
Is he correct? Explain your answer by finding the sample space for the dice differences and using theoretical probability. (4 marks)
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`text(Sample space for dice differences)`
`text(Juan is correct. The table shows Experiment 1)`
`text(has greater total differences to the expected)`
`text(frequencies than Experiment 2)`
A wheel has the numbers 1 to 20 on it, as shown in the diagram. Each time the wheel is spun, it stops with the marker on one of the numbers.
The wheel is spun 120 times.
How many times would you expect a number less than 6 to be obtained?
A spinner with different coloured sectors is spun 40 times. The results are recorded in the table.
What is the relative frequency of obtaining the colour orange?
In an experiment, a standard six-sided die was rolled 72 times. The results are shown in the table.
Which number on the die was obtained the expected number of times?