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Probability, SM-Bank 045

Albert has 50 marbles in a bag.

He records the colour of each marble in the table below.

\begin{array} {|c|c|}
\hline
\rule{0pt}{2.5ex} \textbf{Marble} \rule[-1ex]{0pt}{0pt} & \textbf{Number of Marbles} \\
\hline
\rule{0pt}{2.5ex} \text{Blue} \rule[-1ex]{0pt}{0pt} & \text{20} \\
\hline
\rule{0pt}{2.5ex} \text{Red} \rule[-1ex]{0pt}{0pt} & \text{12} \\
\hline
\rule{0pt}{2.5ex} \text{Orange} \rule[-1ex]{0pt}{0pt} & \text{4} \\
\hline
\rule{0pt}{2.5ex} \text{White} \rule[-1ex]{0pt}{0pt} & \text{?} \\
\hline
\rule{0pt}{2.5ex} \textbf{TOTAL} \rule[-1ex]{0pt}{0pt} & \textbf{50} \\
\hline
\end{array}

  1. What percentage of the marbles are white?  (1 mark)

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

  2. If Albert draws a marble from the bag at random, what is the probability that the marble will be orange or white? Give your answer as a fraction in simplest form.  (2 marks)

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

Show Answers Only

a.    \(28\%\)

b.    \(\dfrac{9}{25}\)

Show Worked Solution

a.    \(\text{Number of white marbles}\)

 \(=50-(20+12+4)\)

\(=14\)

\(\therefore\ \%\text{ white}\) \(=\dfrac{14}{50}\times 100\)
  \(=28\%\)
b.    \(P\text{(Orange or white)}\) \(=\dfrac{\text{number orange and white}}{\text{total number of marbles}}\)
    \(=\dfrac{4+14}{50}=\dfrac{18}{50}\)
    \(=\dfrac{9}{25}\)

Filed Under: Probability Tagged With: num-title-ct-core, smc-4225-15-Single-stage events

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