The pie chart shows the favourite film type of \(180\) people. The sector angles are comedy \(144^\circ\), action \(96^\circ\), drama \(72^\circ\) and horro...
Question 1 Report
The pie chart shows the favourite film type of \(180\) people. The sector angles are comedy \(144^\circ\), action \(96^\circ\), drama \(72^\circ\) and horror \(48^\circ\).
(a) One of these people is chosen at random. Find the probability that drama is their favourite film type. [2]
(b) Work out the number of these people whose favourite film type is comedy. [2]
Answer Details
(a) In a pie chart the full turn of \(360^\circ\) represents all \(180\) people, so the fraction of the circle in a sector is the probability of that category.
\[ P(\text{drama}) = \frac{72}{360} \] [M1]
\[ = \frac{1}{5} \] [A1]
(b) To turn a sector angle into a number of people, apply its fraction of the circle to the total number of people.
\[ \frac{144}{360} \times 180 \] [M1]
\[ = 0.4 \times 180 = 72 \text{ people} \] [A1]
Equivalent forms such as \(\frac{72}{360}\) or \(0.2\) are accepted in (a). Notice that here each person corresponds to \(360 \div 180 = 2^\circ\), so dividing the sector angle by \(2\) gives the same answer of \(72\) people. The angles \(144^\circ + 96^\circ + 72^\circ + 48^\circ\) total \(360^\circ\), confirming the chart accounts for everyone.
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