What is the probability of favourite colour not being red or blue?

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Solution

Q.
A survey was conducted at a high school, and the results were displayed in a circle graph. The students were asked to list their favourite colours. The measurement of each central angle is shown. If a person is chosen at random from the school, find the probability of each response.

Based on the above information, answer the following questions:

(iii) (a) What is the probability of favourite colour not being red or blue

1 0.1

2 0.2

3 0.4

4 0.7

Ans.
(4)

Central angle for favourite colour being red or blue
= central angle for favourite colour being red + central angle for favourite colour being blue

$= 36^{\circ} + 72^{\circ} = 108^{\circ}$

Probability of favourite colour not being red or blue

$= 1 - probability of favourite colour being red or blue = 1 - \frac{A r e a o f r e g i o n o f f a v o u r i t e c o l o u r b e i n g r e d o r b l u e}{A r e a o f c i r c l e} = 1 - \frac{\frac{108 °}{360 °} \times π r^{2}}{π r^{2}} = 1 - \frac{3}{10} = 1 - \frac{\frac{108 °}{360 °} \times π r^{2}}{π r^{2}} = 1 - \frac{3}{10} = \frac{7}{10} = 0.7$

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