Probability, SM-Bank 069

Wendy has a number of different types of flowers as shown in the table below.

\begin{array} {|c|c|}
\hline
\rule{0pt}{2.5ex} \textbf{Type of Flower} \rule[-1ex]{0pt}{0pt} & \textbf{Number of Flowers} \\
\hline
\rule{0pt}{2.5ex} \text{Carnation} \rule[-1ex]{0pt}{0pt} & 8 \\
\hline
\rule{0pt}{2.5ex} \text{Tulip} \rule[-1ex]{0pt}{0pt} & 6 \\
\hline
\rule{0pt}{2.5ex} \text{Dandelion} \rule[-1ex]{0pt}{0pt} & 10 \\
\hline
\rule{0pt}{2.5ex} \text{Rose} \rule[-1ex]{0pt}{0pt} & 8 \\
\hline
\end{array}

What is the probability that a randomly selected flower will be either a carnation or a tulip? (2 marks)
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What is the probability that a randomly selected flower will not be a rose? (2 marks)
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Show Answers Only

a. \(\dfrac{7}{16}\)

b. \(\dfrac{3}{4}\)

Show Worked Solution

a.	\(P\text{(carnation or tulip)}\)	\(=\dfrac{\text{number carnations + number tulips}}{\text{total number of flowers}}\)
		\(=\dfrac{8+6}{32}\)
		\(=\dfrac{14}{32}=\dfrac{7}{16}\)

b.	\(P\text{(not a rose)}\)	\(=1-P\text{(is a rose)}\)
		\(=1-\dfrac{\text{number roses}}{\text{total number of flowers}}\)
		\(=1-\dfrac{8}{32}\)
		\(=1-\dfrac{1}{4}\)
		\(=\dfrac{3}{4}\)